BAYONNE BANCSHARES INC
SC 13D, 1998-07-30
SAVINGS INSTITUTIONS, NOT FEDERALLY CHARTERED
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                                 UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C.  20549

                                 SCHEDULE 13D


                   UNDER THE SECURITIES EXCHANGE ACT OF 1934
                           (AMENDMENT NO. _______)*



                            Bayonne Bancshares, Inc.
- --------------------------------------------------------------------------------
                                (Name of Issuer)


                    Common Stock, par value $0.01 per share
- --------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    072883101
- --------------------------------------------------------------------------------
                                 (CUSIP Number)

  Michael F. Manzulli, Richmond County Financial Corp., 1214 Castleton Avenue,
                           Staten Island, NY  10310
- --------------------------------------------------------------------------------
(Name, Address and Telephone Number of Person Authorized to Receive Notices and
                                Communications)

                                  July 19, 1998
- --------------------------------------------------------------------------------
            (Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition that is the subject of this Schedule 13D, and is filing this
schedule because of (S)(S) 240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the
following box [_].

Note:  Schedules filed in paper format shall include a signed original and five
copies of the schedule.  See (S) 240.13d-7(b) for other parties to whom copies
are to be sent.

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).
<PAGE>
 
<TABLE> 
<CAPTION> 
                                                              SCHEDULE 13D
- -----------------------                                  
  CUSIP NO. 072883101                                    
- -----------------------                                  
- -----------------------------------------------------------------------------------------------------------------------------------
<S>                                                                      <C>   
      NAME OF REPORTING PERSON
 1    S.S. OR I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)
                          
      RICHMOND COUNTY FINANCIAL CORP.

      I.R.S. Employer Indemnification No.: 06-1998455
- -----------------------------------------------------------------------------------------------------------------------------------
      CHECK BOX IF A MEMBER OF A GROUP
 2                                                              (a) [_]
                                                                (b) [_]
- -----------------------------------------------------------------------------------------------------------------------------------
      SEC USE ONLY
 3
- -----------------------------------------------------------------------------------------------------------------------------------
      SOURCE OF FUNDS*
 4    
      WC (No shares have been purchased yet; see items 3 and 4).
- -----------------------------------------------------------------------------------------------------------------------------------
 5    CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
      TO ITEMS 2(d) or 2(e)                                               [_]
      
- -----------------------------------------------------------------------------------------------------------------------------------
      CITIZENSHIP OR PLACE OF ORGANIZATION
 6    Delaware
      
- -----------------------------------------------------------------------------------------------------------------------------------
                          SOLE VOTING POWER
                     7    2,252,304*
     NUMBER OF            
                             
      SHARES       -----------------------------------------------------------
                          SHARED VOTING POWER
   BENEFICIALLY      8         0
                          
     OWNED BY                    
                   -----------------------------------------------------------
       EACH               SOLE DISPOSITIVE POWER
                     9    2,252,304*
    REPORTING             
                         
      PERSON       -----------------------------------------------------------
                          SHARED DISPOSITIVE POWER
       WITH          10        0
                                 
- -----------------------------------------------------------------------------------------------------------------------------------
      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
11    2,252,304*
- -----------------------------------------------------------------------------------------------------------------------------------
      CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES
12                  
      [_]
- -----------------------------------------------------------------------------------------------------------------------------------
      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11); 20.7%
13    
- -----------------------------------------------------------------------------------------------------------------------------------
      TYPE OF REPORTING PERSON
14    CO;HC
- -----------------------------------------------------------------------------------------------------------------------------------

*  As of the date of the filing of this Schedule 13D, Richmond County Financial Corp. ("Richmond County") beneficially owns 442,500
shares of Bayonne Bancshares, Inc. ("Bayonne") Common Stock. Additionally, pursuant to the Stock Option Agreement entered into by
and between Richmond County and Bayonne as of July 19, 1998 (the "Stock Option Agreement"), as an inducement for the parties to
enter into the Agreement and Plan of Merger dated as of July 19, 1998 by and between Richmond County Financial Corp. and Bayonne
Bancshares, Inc., Richmond County may have the option to purchase (the "Option"), and therefore may be the beneficial owner of, an
additional 1,809,804 shares of Bayonne Common Stock. The Option may only be exercised upon the occurrence of certain events, as
further referred to in Item 4 and as fully described in the Stock Option Agreement attached hereto as Exhibit 10.1, none of which
has occurred as of the date hereof. Richmond County expressly disclaims beneficial ownership of any of the shares of Bayonne which
are purchasable upon exercise of the Option.
</TABLE>
                                  2 OF 13 
<PAGE>
 
Item 1.   Security and Issuer.
          ------------------- 

     This statement relates to the common stock, par value $0.01 per share (the
"Common Stock"), of Bayonne Bancshares, Inc. ("Bayonne").  The principal
executive office of Bayonne Bancshares, Inc. is located at 568 Broadway,
Bayonne, New Jersey 07002.

Item 2.   Identity and Background.
          ----------------------- 

     This Schedule 13D is being filed by Richmond County Financial Corp.
("Richmond County"), a Delaware corporation, which is the holding company for
Richmond County Savings Bank (the "Bank").  Richmond County's principal business
is the business of the Bank.  The principal office of Richmond County is located
at 1214 Castleton Avenue, Staten Island, New York 10310.  During the past five
years, Richmond County has not been convicted in a criminal proceeding
(excluding traffic violations or similar misdemeanors) or been a party to a
civil proceeding of a judicial or administrative body of competent jurisdiction
and has not as a result of such proceeding been subject to a judgment, decree or
final order enjoining future violations of, or prohibiting or mandating
activities subject to, federal or state securities laws or finding any violation
with respect to such laws.

     Attached as Schedule I hereto and incorporated herein by reference is a
                 ----------                                                 
list containing the (a) name, (b) business or residential address, and (c)
present principal occupation or employment and the name, principal business and
address of any corporation or other organization in which such employment is
conducted, of each director and executive officer of Richmond County.  To
Richmond County's knowledge, each of the directors and executive officers of
Richmond County is a United States citizen, and none of such directors and
executive officers has, during the past five years, been convicted in a criminal
proceeding (excluding traffic violations or similar misdemeanors) or been a
party to a civil proceeding of a judicial or administrative body of competent
jurisdiction and as a result of such proceeding was or is subject to a judgment,
decree or final order enjoining future violations of, or prohibiting or
mandating activities subject to, federal or state securities laws or finding any
violation with respect to such laws.

Item 3.   Source and Amount of Funds or Other Consideration.
          --------------------------------------------------

     As summarized in Item 4 and as fully described in the Stock Option
Agreement attached hereto as Exhibit 10.1, Bayonne has granted to Richmond
County an option pursuant to which Richmond County has the right, upon the
occurrence of certain events (none of which has occurred), to purchase 1,809,804
shares of Bayonne Common Stock (subject to adjustment in certain circumstances)
at a price of $15.50 per share (the "Option").  If the Option was exercisable
and Richmond County was to exercise the Option on the date hereof, the funds
required to purchase the shares issuable upon such exercise would be
approximately $28,051,962.  It is currently anticipated that such funds would be
derived from working capital.

                                    3 of 13
<PAGE>
 
Item 4.   Purpose of Transaction/1/.
          --------------------------

     Richmond County is seeking to acquire Bayonne pursuant to the Agreement and
Plan of Merger dated as of July 19, 1998 by and between Richmond County
Financial Corp. and Bayonne Bancshares, Inc. (the "Merger Agreement," a copy of
which is attached hereto as Exhibit 2.1).  The Merger Agreement provides for,
among other things, the merger of Bayonne with and into Richmond County, with
Richmond County being the surviving corporation (the "Merger").  At the
effective time of the Merger (the "Effective Time"), each outstanding share of
Bayonne Common Stock becomes and converts into the right to receive 1.05 shares
of Richmond County Common Stock.

     Consummation of the Merger is subject to the satisfaction of certain
conditions set forth in the Merger Agreement, including approval of the
shareholders of both Richmond County and Bayonne, and the approval of
appropriate regulatory agencies.

     Concurrently with the execution of the Merger Agreement, Richmond County
and Bayonne entered into a Stock Option Agreement, dated as of July 19, 1998
(the "Stock Option Agreement"). The Stock Option Agreement is designed to
enhance the likelihood that the Merger will be successfully consummated in
accordance with the terms contemplated by the Merger Agreement and Richmond
County insisted on such agreement for that reason.  Pursuant to the Stock Option
Agreement, Bayonne granted Richmond County the option to purchase authorized but
unissued shares (the "Option Shares") of up to 19.9% of the then outstanding
shares of Bayonne stock at a price of $15.50 per share, subject to adjustment in
certain circumstances (the "Option").

     Provided that (i) Richmond County shall not be in material breach of the
agreements or covenants contained in the Merger Agreement or the Stock Option
Agreement and (ii) no preliminary or permanent injunction or other order against
the delivery of the shares covered by the Option issued by any court of
competent jurisdiction in the United States shall be in effect, Richmond County
may exercise the Option, in whole or in part, at any time and from time to time,
following the occurrence of a Purchase Event (as defined below); provided that
the Option shall terminate and be of no further force or effect upon the
earliest to occur of (A) the Effective Time, (B) termination of the Merger
Agreement by Bayonne in accordance with the terms thereof prior to the
occurrence of a Purchase Event or a Preliminary Purchase Event (as defined
below) (an "Issuer Termination"), (C) 12 months after the termination of the
Merger Agreement by Bayonne other than pursuant to an Issuer Termination, (D)
12 months after termination of the Merger Agreement, and (E) 12 months after the
first occurrence of a Purchase Event, provided, however, that any purchase of
shares upon exercise of the Option shall be subject to certain restrictions,
including compliance with applicable law.

- -----------------------
/1/  Unless otherwise designated, all capitalized terms used in this filing
shall have the meanings ascribed such terms in the Bayonne Stock Option
Agreement dated as of July 19, 1998 attached hereto as Exhibit 10.1.

                                    4 of 13
<PAGE>
 
     A "Purchaser Event" means any of the following events:

     (a) Without Richmond County's prior written consent, Bayonne shall have
authorized, recommended, publicly proposed or publicly announced an intention to
authorize, recommend or propose, or entered into an agreement with any person
(other than Richmond County or any subsidiary of Richmond County) to effect an
Acquisition Transaction. As used in the Stock Option Agreement, the term
"Acquisition Transaction" shall mean (i) a merger, consolidation or similar
transaction involving Bayonne or any of its significant subsidiaries, (ii) the
disposition, by sale, lease, exchange or otherwise, of assets or deposits of
Bayonne or any of its significant subsidiaries representing in either case 20%
or more of the consolidated assets or deposits of Bayonne and its subsidiaries,
or (iii) the issuance, sale or other disposition of (including by way of merger,
consolidation, share exchange or any similar transaction) securities
representing 15% or more of the voting power of Bayonne or any of its
significant subsidiaries other than the issuance of Bayonne Common Stock upon
the exercise of outstanding options; or

     (b) any person (other than Richmond County or any subsidiary of Richmond
County) shall have acquired beneficial ownership (as such term is defined in
Rule 13d-3 promulgated under the Securities Exchange Act of 1934 (the "Exchange
Act")) of or the right to acquire beneficial ownership of, or any "group" (as
such term is defined under the Exchange Act) shall have been formed which
beneficially owns or has the right to acquire beneficial ownership of, 15% or
more of the voting power of Bayonne or any of its significant subsidiaries.

     As used in the Stock Option Agreement, a "Preliminary Purchase Event" means
any of the following events:

     (a) any person (other than Richmond County or any subsidiary of Richmond
County) shall have commenced (as such term is defined in Rule 14d-2 under the
Exchange Act), or shall have filed a registration statement under the Securities
Act with respect to, a tender offer or exchange offer to purchase any shares of
Bayonne Common Stock such that, upon consummation of such offer, such person
would own or control 15% or more of the then outstanding shares of Bayonne
Common Stock (such an offer being referred to in the Stock Option Agreement as a
"Tender Offer" or an "Exchange Offer," respectively); or

     (b) the holders of Bayonne Common Stock shall not have approved the Merger
Agreement at the Bayonne Stockholders' Meeting, the Meeting shall not have been
held or shall have been canceled prior to termination of the Merger Agreement,
or Bayonne's Board of Directors shall have withdrawn or modified in a manner
adverse to Richmond County the recommendation of Bayonne's Board of Directors
with respect to the Merger Agreement, in each case after it shall have been
publicly announced that any person (other than Richmond County or any subsidiary
of Richmond County) shall have (A) made or disclosed an intention to make a
proposal to engage in an Acquisition Transaction, or (B) commenced a Tender
Offer or filed a registration statement under the Securities Act with respect to
an Exchange Offer; or

                                    5 of 13
<PAGE>
 
     (c) any person, other than Richmond County or any subsidiary of Richmond
County, shall have made a bona fide proposal to Bayonne or its stockholders by
public announcement, or written communication that is or becomes the subject of
public disclosure, to engage in an Acquisition Transaction; or

     (d) after a bona fide proposal is made by a third party to Bayonne or its
stockholders to engage in an Acquisition Transaction, Bayonne shall have
breached any covenant or obligation contained in the Merger Agreement and such
breach would entitle Richmond County to terminate the Merger Agreement under
Section 6.1(h) thereof (without regard to the cure period provided for therein
unless such cure is promptly effected without jeopardizing consummation of the
Merger pursuant to the terms of the Merger Agreement); or

     (e) any person, other than Richmond County or any subsidiary of Richmond
County, other than in connection with a transaction to which Richmond County has
given its prior written consent, shall have filed an application or notice with
the Office of Thrift Supervision (the "OTS"), or other federal or state bank
regulatory authority, for approval to engage in an Acquisition Transaction.

     Bayonne shall notify Richmond County promptly in writing of the occurrence
of any Preliminary Purchase Event or Purchase Event.

     In the event Holder (meaning the Holder of the Option from time to time,
the initial Holder being Richmond County) wishes to exercise the Option, it
shall send to Bayonne a written notice (the date of which is the "Notice Date")
specifying (i) the total number of Option Shares it intends to purchase pursuant
to such exercise, and (ii) a place and date not earlier than three business days
nor later than 15 business days from the Notice Date for the closing (the
"Closing") of such purchase (the "Closing Date"); PROVIDED, HOWEVER, if any
required application for listing such shares on the Nasdaq National Market has
not been approved by the date so specified, such date shall be extended for a
period not to exceed 21 days from the Notice Date.  If prior notification to or
approval of the OTS or any other regulatory authority is required in connection
with such purchase, Bayonne shall cooperate with the Holder in the filing of the
required notice or application for approval and the obtaining of such approval
and the Closing shall occur immediately following such regulatory approvals (and
any mandatory waiting periods). Any exercise of the Option shall be deemed to
occur on the Notice Date relating thereto.

     Bayonne agrees (i) that it shall at all times maintain, free from
preemptive rights, sufficient authorized but unissued or treasury shares of
Bayonne Common Stock so that the Option may be exercised without additional
authorization of Bayonne Common Stock after giving effect to all other options,
warrants, convertible securities and other rights to purchase Bayonne Common
Stock, (ii) that it will not, by charter amendment or through reorganization,
consolidation, merger, dissolution or sale of assets, or by any other voluntary
act, avoid or seek to avoid the observance or performance of any of the
covenants, stipulations or conditions to be observed or performed under the
Stock Option Agreement by Bayonne, (iii) promptly to take all action as may from
time to time be required 

                                    6 of 13
<PAGE>
 
(including (A) complying with all premerger notification, reporting and waiting
period requirements specified in 15 U.S.C. (S)18a and regulations promulgated
thereunder and (B) in the event, under the HOLA, or the Change in Bank Control
Act of 1978, as amended, or a state banking law, prior approval of or notice to
the OTS or to any state regulatory authority is necessary before the Option may
be exercised, cooperating fully with Holder in preparing such applications or
notices and providing such information to the OTS or such state regulatory
authority as they may require) in order to permit Holder to exercise the Option
and Bayonne duly and effectively to issue shares of the Bayonne Common Stock
pursuant to the Stock Option Agreement, and (iv) promptly to take all action
provided in the Stock Option Agreement to protect the rights of Holder against
dilution.

     In the event of any change in Bayonne Common Stock by reason of a stock
dividend, stock split, split-up, recapitalization, combination, exchange of
shares or similar transaction, the type and number of shares or securities
subject to the Option, and the purchase price therefor, shall be adjusted
appropriately, and proper provision shall be made in the agreements governing
such transaction so that Holder shall receive, upon exercise of the Option, the
number and class of shares or other securities or property that Holder would
have received in respect of Bayonne Common Stock if the Option had been
exercised immediately prior to such event, or the record date therefor, as
applicable. If any additional shares of Bayonne Common Stock are issued after
the date of the Stock Option Agreement (other than pursuant to an event
described in the first sentence of this paragraph, upon exercise of any option
to purchase Bayonne Common Stock outstanding on the date hereof, or upon
conversion into Bayonne Common Stock of any convertible security of Bayonne
outstanding on the date of the Stock Option Agreement), the number of shares of
Bayonne Common Stock subject to the Option shall be adjusted so that, after such
issuance, it, together with any shares of Bayonne Common Stock previously issued
pursuant to the Stock Option Agreement, equals 19.9% of the number of shares of
Bayonne Common Stock then issued and outstanding, without giving effect to any
shares subject to or issued pursuant to the Option.

     In the event that Bayonne shall enter in an agreement (i) to consolidate
with or merge into any person, other than Richmond County or one of its
subsidiaries, and shall not be the continuing or surviving corporation of such
consolidation or merger, (ii) to permit any person, other than Richmond County
or one of its subsidiaries, to merge into Bayonne and Bayonne shall be the
continuing or surviving corporation, but, in connection with such merger, the
then outstanding shares of Bayonne Common Stock shall be changed into or
exchanged for stock or other securities of Bayonne or any other person or cash
or any other property or the outstanding shares of Bayonne Common Stock
immediately prior to such merger shall after such merger represent less than 50%
of the outstanding shares and share equivalents of the merged company, or (iii)
to sell or otherwise transfer all or substantially all of its assets to any
person, other than Richmond County or one of its subsidiaries, then, and in each
such case, the agreement governing such transaction shall make proper provisions
so that the Option shall, upon the consummation of any such transaction and upon
the terms and conditions set forth herein, be converted into, or exchanged for,
an option (the "Substitute Option"), at the election of Holder, of either (x)
the Acquiring Corporation (as hereinafter defined), (y) any person that controls
the Acquiring Corporation, or (z) in the case of a merger described in clause
(ii) above, Bayonne (such person being referred to as "Substitute Option
Issuer").

                                    7 of 13
<PAGE>
 
     Bayonne will not enter into any transaction described in the paragraph
above unless the Acquiring Corporation, and any person that controls the
Acquiring Corporation, assumes in writing all the obligations of Bayonne under
the Stock Option Agreement.

     The Substitute Option shall have the same terms as the Option, provided,
that, if the terms of the Substitute Option cannot, for legal reasons, be the
same as the Option, such terms shall be as similar as possible and in no event
less advantageous to Holder. Substitute Option Issuer shall also enter into an
agreement with Holder in substantially the same form as the Stock Option
Agreement, which shall be applicable to the Substitute Option.

          "Acquiring Corporation" means (i) the continuing or surviving
corporation of a consolidation or merger with Bayonne (if other than Bayonne),
(ii) Bayonne in a merger in which Bayonne is the continuing or surviving person,
or (iii) the transferee of all or substantially all of Bayonne's assets (or a
substantial part of the assets of its subsidiaries taken as a whole).

     Bayonne shall, subject to certain conditions as hereinafter defined, if
requested by any Holder or Owner, as applicable, including Richmond County and
any permitted transferee ("Selling Shareholder"), as expeditiously as possible
prepare and file a registration statement under the Securities Act if such
registration is necessary in order to permit the sale or other disposition of
any or all shares of Bayonne Common Stock or other securities that have been
acquired by or are issuable to the Selling Shareholder upon exercise of the
Option in accordance with the intended method of sale or other disposition
stated by the Selling Shareholder in such request, including without limitation
a "shelf" registration statement under Rule 415 under the Securities Act or any
successor provision, and Bayonne shall use its best efforts to qualify such
shares or other securities for sale under any applicable state securities laws.
Richmond County shall have the right to demand no more than two registrations as
described in this paragraph.  If requested by Richmond County in connection with
any such registration, Bayonne and Richmond County shall provide each other with
representations, warranties, indemnities and other agreements customarily given
in connection with such registration.  If requested by Richmond County in
connection with any such registration, Bayonne and Richmond County shall become
party to any underwriting agreement relating to the sale of the Option Shares,
but only to the extent of obligating themselves in respect of representations,
warranties, indemnities and other agreement customarily included in such
underwriting agreements.

     Bayonne shall use all reasonable efforts to cause each registration
statement referred to above to become effective and to obtain all consents or
waivers of other parties which are required therefor and to keep such
registration statement effective, PROVIDED, HOWEVER, that Bayonne may delay any
registration of Option Shares described in the preceding paragraph for a period
not exceeding 180 days provided Bayonne shall in good faith determine that any
such registration would adversely affect an offering or contemplated offering of
other securities by Bayonne, and Bayonne shall not be required to register
Option Shares under the Securities Act:

                                    8 of 13
<PAGE>
 
          (i)   prior to the earliest of (a) termination of the Merger Agreement
     pursuant to Section 6.1 thereof, (b) failure to obtain the requisite
     stockholder approval pursuant to Section 4.8 of the Merger Agreement, and
     (c) a Purchase Event or a Preliminary Purchase Event;

          (ii)  on more than one occasion during any calendar year;

          (iii) within 90 days after the effective date of a registration
     referred to above pursuant to which the Selling Shareholder or Selling
     Shareholders concerned were afforded the opportunity to register such
     shares under the Securities Act and such shares were registered as
     requested; and

          (iv)  unless a request therefor is made to Bayonne by Selling
     Shareholders that hold at least 25% or more of the aggregate number of
     Option Shares (including shares of Bayonne Common Stock issuable upon
     exercise of the Option) then outstanding.

     The foregoing description is qualified in its entirety by reference to the
Merger Agreement and the Stock Option Agreement themselves, copies of which are
attached hereto as Exhibits 2.1 and 10.1, respectively.

Item 5.   Interest in Securities of Bayonne.
          --------------------------------- 

     (a)  (i)   Richmond County is the beneficial owner of 442,500 shares;

          (ii)  Richmond County also may be deemed to be the beneficial owner of
the Option Shares.  As provided in the Stock Option Agreement, Richmond County
may exercise the Option only upon the happening of one or more events, none of
which has occurred.  See Item 4 hereof.  Because the Option is not presently
exercisable, Richmond County expressly disclaims beneficial ownership of any of
the Option Shares.  If the Option was exercised in full, the Option Shares would
represent approximately 16.6% of the currently outstanding shares (after giving
effect to the issuance of such Option Shares).  Richmond County has no right to
vote or dispose of the shares subject to the Option unless and until such time
as the Option is exercised.  To the best knowledge of Richmond County, none of
the persons listed on Schedule I hereto beneficially owns any shares of Bayonne
Common Stock.

     (b)  (i)   Richmond County has sole power to vote or direct the vote and
sole power to dispose or direct the disposition of 442,500 shares of Bayonne
Common Stock;

          (ii)  If Richmond County were to exercise the Option, it would have
sole power to vote and, subject to the terms of the Stock Option Agreement, sole
power to direct the disposition of 2,252,304 shares of Bayonne Bancshares, Inc.
Common Stock.

                                    9 of 13
<PAGE>
 
     (c) Richmond County acquired the Option on July 19, 1998 in connection with
the execution of the Merger Agreement and the Stock Option Agreement, both of
which are attached hereto as Exhibits 2.1 and 10.1, respectively.  See Item 4
hereof.

     To the best knowledge of Richmond County, none of the persons listed on
Schedule I hereto has effected any transactions in the shares during the past 60
days.

     (d) No person other than Richmond County has the right to receive or the
power to direct the receipt of dividends from, or the proceeds from the sale of,
any shares of Bayonne Common Stock that may be deemed beneficially owned by
Richmond County on account of the Option.

     (e)  Not applicable.

Item 6.   Contracts, Arrangements, Understandings or Relationship with Respect
          --------------------------------------------------------------------
          to Securities of Bayonne.
          ------------------------ 

     As described in Item 4 above and filed as Exhibits 2.1 and 10.1 hereto,
Richmond County has entered into the Merger Agreement and the Stock Option
Agreement with Bayonne Bancshares, Inc.  Other than the foregoing, or as
referred to in the foregoing, there are no contracts, arrangements,
understandings or relationships (legal or otherwise) among the persons named in
Item 2 of this statement or between such persons and any person with respect to
any securities of Bayonne Bancshares, Inc.

Item 7.   Material to be Filed as Exhibits.
          -------------------------------- 

          Exhibit 2.1 -       Agreement and Plan of Merger, dated as of July 19,
                              1998, by and between Richmond County Financial
                              Corp. and Bayonne Bancshares, Inc.

          Exhibit 10.1 -      Stock Option Agreement, dated as of July 19, 1998,
                              by and between Richmond County Financial Corp. and
                              Bayonne Bancshares, Inc.

                                   10 of 13
<PAGE>
 
                                   SIGNATURE
                                   ---------

     After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.


                                    RICHMOND COUNTY FINANCIAL
                                        CORP.



                                    By:  /s/ Michael F. Manzulli
                                       -----------------------------------------
                                         Michael F. Manzulli
                                         President and Chief Executive Officer

Date:  July 29, 1998

                                   11 of 13
<PAGE>
 
                                   Schedule I

      Directors and Executive Officers of Richmond County Financial Corp.
      ------------------------------------------------------------------ 

     The names, business address and present principal occupation of each
director, executive officer and controlling person of Richmond County Financial
Corp. are set forth below.  Unless otherwise indicated, all persons are citizens
of the United States.

<TABLE>
<CAPTION>
NAME                          BUSINESS ADDRESS                 PRINCIPAL OCCUPATION
- ----                          ----------------                 --------------------
 
DIRECTORS:
 
<S>                           <C>                              <C>
Michael F. Manzulli           1214 Castleton Avenue            Chairman of the Board of Directors and Chief Executive
                              Staten Island, New York  10310   Officer of Richmond County Financial Corp., and
                                                               Director, President and Chief Executive Officer of
                                                               Richmond County Savings Bank.
 
Anthony E. Burke              1214 Castleton Avenue            President, Chief Operating Officer and Director of
                              Staten Island, New York  10310   Richmond County Financial Corp.
 
James L. Kelley               1214 Castleton Avenue            Director of Richmond County Financial Corp. and
                              Staten Island, New York  10310   Director of Richmond County Savings Bank.  Mr. Kelley
                                                               is a partner of the law firm of Lahr, Dillon, Manzulli,
                                                               Kelley & Penett, P.C., which serves as general counsel to
                                                               Richmond County Savings Bank.
 
T. Ronald Quinlan, Jr.        1214 Castleton Avenue            Director of Richmond County Financial Corp. and
                              Staten Island, New York  10310   Director of Richmond County Savings Bank.
 
William C. Frederick          1214 Castleton Avenue            Director of Richmond County Financial Corp. and
                              Staten Island, New York  10310   Director of Richmond County Savings Bank.  Dr.
                                                               Frederick is a surgeon in Staten Island and is affiliated
                                                               with St. Vincent's Hospital, Staten Island University
                                                               Hospital and Bayley Seton Hospital.
 
Maurice K. Shaw               1214 Castleton Avenue            Director of Richmond County Financial Corp. and
                              Staten Island, New York  10310   Director of Richmond County Savings Bank.  Mr. Shaw is
                                                               currently Senior Vice President in charge of corporate
                                                               affairs of Brooklyn Union Gas Co.
 
Godfrey H. Carstens, Jr.      1214 Castleton Avenue            Director of Richmond County Financial Corp. and
                              Staten Island, New York  10310   Director of Richmond County Savings Bank.
                                                               Mr. Carstens is currently the owner and president of
                                                               Carstens Electrical Supply Co., an electrical supply
                                                               company located in Staten Island, New York.
 
Robert S. Farrell             1214 Castleton Avenue            Director of Richmond County Financial Corp. and
                              Staten Island, New York  10310   Director of Richmond County Savings Bank.  Mr. Farrell
                                                               is currently president of H.S. Farrell, Inc., a lumber,
                                                               millwork and building materials supply company located
                                                               in Staten Island, New York.
</TABLE> 

                                   12 of 13
<PAGE>
 
<TABLE>
<CAPTION>
NAME                          BUSINESS ADDRESS                 PRINCIPAL OCCUPATION
- ----                          ----------------                 --------------------

<S>                           <C>                              <C>  
Thomas R. Cangemi             1214 Castleton Avenue            Chief Financial Officer and Secretary of Richmond County
                              Staten Island, New York  10310   Financial Corp.
 
Andrew M. Sisock              1214 Castleton Avenue            Senior Vice President, Senior Financial Officer, and Vice
                              Staten Island, New York  10310   President-Accounting of Richmond County Financial
                                                               Corp.  Mr. Sisock is also a Director and Treasurer of
                                                               Richmond County Savings Bank and Richmond
                                                               Enterprises, Inc.
</TABLE>

                                   13 of 13

<PAGE>
 
                                                        Exhibit 2.1

================================================================================

                          AGREEMENT AND PLAN OF MERGER



                           DATED AS OF JULY 19, 1998



                                 BY AND BETWEEN



                        RICHMOND COUNTY FINANCIAL CORP.



                                      AND



                            BAYONNE BANCSHARES, INC.


================================================================================
<PAGE>
 
                               TABLE OF CONTENTS
<TABLE>
<CAPTION>
                                                                                                    PAGE NO.
<S>                      <C>                                                                          <C>
Introductory Statement                                                                                 4
 
ARTICLE I
     THE MERGER ..................................................................................     5
     ----------
     Section 1.1.        Structure of the Merger .................................................     5
                         -----------------------
     Section 1.2.        Effect on Outstanding Shares of Bayonne Common Stock ....................     5
                         ----------------------------------------------------
     Section 1.3.        Exchange Procedures .....................................................     6
                         -------------------
     Section 1.4.        Stock Options ...........................................................     8
                         -------------
     Section 1.5.        Bank Merger .............................................................     9
                         -----------
     Section 1.6.        Directors of RCFC after Effective Time ..................................     9
                         --------------------------------------
     Section 1.7.        Alternative Structure ...................................................     9
                         ---------------------
     Section 1.8.        Certificate of Incorporation and Bylaws of the Surviving Corporation ....     9
                         --------------------------------------------------------------------
 
ARTICLE II
     REPRESENTATIONS AND WARRANTIES ..............................................................    10
     ------------------------------
     Section 2.1.        Disclosure Letters ......................................................    10
                         ------------------
     Section 2.2.        Standards ...............................................................    10
                         ---------
     Section 2.3.        Representations and Warranties of Bayonne ...............................    11
                         -----------------------------------------
     Section 2.4.        Representations and Warranties of RCFC ..................................    26
                         --------------------------------------
 
ARTICLE III
     CONDUCT PENDING THE MERGER ..................................................................    38
     --------------------------
     Section 3.1.        Conduct of Bayonne's Business Prior to the Effective Time ...............    38
                         ---------------------------------------------------------
     Section 3.2.        Forbearance by Bayonne ..................................................    39
                         ----------------------
     Section 3.3.        Conduct of RCFC's Business Prior to the Effective Time ..................    42
                         ------------------------------------------------------
 
ARTICLE IV
     COVENANTS ...................................................................................    42
     ---------
     Section 4.1.        Acquisition Proposals ...................................................    42
                         ---------------------
     Section 4.2.        Certain Policies of Bayonne .............................................    44
                         ---------------------------
     Section 4.3.        Access and Information ..................................................    44
                         ----------------------
     Section 4.4.        Certain Filings, Consents and Arrangements ..............................    45
                         ------------------------------------------
     Section 4.5.        Antitakeover Provisions .................................................    46
                         -----------------------
     Section 4.6.        Additional Agreements ...................................................    46
                         ---------------------
     Section 4.7.        Publicity ...............................................................    46
                         ---------
     Section 4.8.        Stockholders Meetings ...................................................    46
                         ---------------------
     Section 4.9.        Proxy Statements; Comfort Letters .......................................    47
                         ---------------------------------
     Section 4.10.       Registration of RCFC Common Stock .......................................    47
                         ---------------------------------
     Section 4.11.       Affiliate Letters .......................................................    48
                         -----------------
     Section 4.12.       Notification of Certain Matters .........................................    48
                         -------------------------------
     Section 4.13.       Employees, Directors and Officers .......................................    49
                         ---------------------------------
     Section 4.14.       Indemnification .........................................................    50
                         ---------------
</TABLE> 

                                       2
<PAGE>
 
<TABLE> 
<CAPTION> 
                                                                                                    PAGE NO.
<S>                      <C>                                                                          <C>
     Section 4.15.       Pooling and Tax-Free Reorganization Treatment ...........................    52
                         ---------------------------------------------
     Section 4.16.       Divisional Board ........................................................    52
                         ----------------
 
ARTICLE V
     CONDITIONS TO CONSUMMATION ..................................................................    53
     --------------------------
     Section 5.1.        Conditions to Each Party's Obligations ..................................    53
                         --------------------------------------
     Section 5.2.        Conditions to the Obligations of RCFC and RCFC Bank .....................    54
                         ---------------------------------------------------
     Section 5.3.        Conditions to the Obligations of Bayonne and First Savings ..............    56
                         ----------------------------------------------------------
 
ARTICLE VI
     TERMINATION .................................................................................    57
     -----------
     Section 6.1.        Termination .............................................................    57
                         -----------
     Section 6.2.        Effect of Termination ...................................................    61
                         ---------------------
      
ARTICLE VII
     CLOSING, EFFECTIVE DATE AND EFFECTIVE TIME ..................................................    61
     ------------------------------------------
     Section 7.1.        Effective Date and Effective Time .......................................    61
                         ---------------------------------
     Section 7.2.        Deliveries at the Closing ...............................................    61
                         -------------------------
 
ARTICLE VIII
     CERTAIN OTHER MATTERS .......................................................................    61
     ---------------------
     Section 8.1.        Certain Definitions; Interpretation .....................................    61
                         -----------------------------------
     Section 8.2.        Survival ................................................................    62
                         --------
     Section 8.3.        Waiver; Amendment .......................................................    62
                         -----------------
     Section 8.4.        Counterparts ............................................................    62
                         ------------
     Section 8.5.        Governing Law ...........................................................    62
                         -------------
     Section 8.6.        Expenses ................................................................    62
                         --------
     Section 8.7.        Notices .................................................................    63
                         -------
     Section 8.8.        Entire Agreement; etc ...................................................    64
                         ---------------------
     Section 8.9.        Assignment ..............................................................    64
                         ----------

</TABLE>

                                       3
<PAGE>
 
                          AGREEMENT AND PLAN OF MERGER
                          ----------------------------


          This is an AGREEMENT AND PLAN OF MERGER, dated as of the 19/th/ day of
July, 1998 ("Agreement"), by and between Richmond County Financial Corp., a
Delaware corporation ("RCFC"), and Bayonne Bancshares, Inc., a Delaware
corporation ("Bayonne").

                             INTRODUCTORY STATEMENT

          The Board of Directors of each of RCFC and Bayonne (i) has determined
that this Agreement and the business combination and related transactions
contemplated hereby are in the best interests of RCFC and Bayonne, respectively,
and in the best long-term interests of their respective stockholders, (ii) has
determined that this Agreement and the transactions contemplated hereby are
consistent with, and in furtherance of, its respective business strategies and
(iii) has approved, at meetings of each of such Boards of Directors, this
Agreement.

          Concurrently with the execution and delivery of this Agreement, and as
a condition and inducement to RCFC's willingness to enter into this Agreement,
RCFC and Bayonne have entered into a stock option agreement (the "Option
Agreement"), pursuant to which Bayonne has granted to RCFC an option to purchase
shares of Bayonne's common stock, par value $0.01 per share ("Bayonne Common
Stock"), upon the terms and conditions therein contained; and Bayonne will use
its best efforts to have certain executive officers and directors of Bayonne,
within twenty-one days of the date of this Agreement, execute in favor of RCFC a
Letter Agreement in the form annexed as Exhibit A.

          The parties hereto intend that the Merger as defined herein shall
qualify as a reorganization under the provisions of Section 368(a) of the
Internal Revenue Code of 1986, as amended ("Code"), for federal income tax
purposes, and that the Merger shall be accounted for as a pooling-of-interests
for accounting purposes.

          RCFC and Bayonne desire to make certain representations, warranties
and agreements in connection with the business combination and related
transactions provided for herein and to prescribe various conditions to such
transactions.

          In consideration of their mutual promises and obligations hereunder,
the parties hereto adopt and make this Agreement and prescribe the terms and
conditions hereof and the manner and basis of carrying it into effect, which
shall be as follows:

                                       4
<PAGE>
 
                                   ARTICLE I
                                   THE MERGER
                                   ----------

          Section 1.1.   Structure of the Merger.  On the Effective Date (as
                         -----------------------                            
defined in Section 7.1), Bayonne will merge with and into RCFC ("Merger"), with
RCFC being the surviving entity, pursuant to the provisions of, and with the
effect provided in, the Delaware General Corporation Law ("DGCL").  Upon
consummation of the Merger, the separate corporate existence of Bayonne shall
cease.  RCFC shall continue to be governed by the laws of the State of Delaware
and its name and separate corporate existence, with all of its rights,
privileges, immunities, powers and franchises, shall continue unaffected by the
Merger.  From and after the Effective Time, RCFC shall possess all of the
properties and rights and subject to all of the liabilities and obligations of
Bayonne, all as more fully described in the DGCL.

          Section 1.2.   Effect on Outstanding Shares of Bayonne Common Stock.
                         ---------------------------------------------------- 

          (a)  By virtue of the Merger, automatically and without any action on
the part of the holder thereof, each share of Bayonne Common Stock issued and
outstanding at the Effective Time (as defined in Section 7.1), other than (i)
shares the holder of which (the "Dissenting Shareholders") pursuant to any
applicable law providing for dissenters' or appraisal rights is entitled to
receive payment in accordance with the provisions of any such law, such holder
to have only the rights provided in any such law (the "Dissenters' Shares"),
(ii) shares held directly or indirectly by RCFC (other than shares held in a
fiduciary capacity or in satisfaction of a debt previously contracted), (iii)
shares held by Bayonne as treasury stock and (iv) unallocated shares held in the
Amended and Restated Bayonne Bancshares, Inc. 1995 Recognition and Retention
Plan ("Bayonne RRP") (such shares referred to in clauses (i), (ii), (iii) and
(iv) being referred to herein as the "Excluded Shares") shall become and be
converted into the right to receive 1.05 shares of RCFC Common Stock (the
"Exchange Ratio"); provided, however, that, notwithstanding any other provision
hereof, no fraction of a share of RCFC Common Stock and no certificates or scrip
therefor will be issued in the Merger; instead, RCFC shall pay to each holder of
Bayonne Common Stock who would otherwise be entitled to a fraction of a share of
RCFC Common Stock an amount in cash, rounded to the nearest cent, determined by
multiplying such fraction by the RCFC Market Value (as defined herein)
(collectively, the "Merger Consideration").

          (b)  As used herein, "RCFC Market Value" shall be the average of the
closing sales price on that day, as reported on the National Market System of
The Nasdaq Stock Market, Inc. ("Nasdaq National Market"), for the 15 consecutive
trading days immediately preceding the day on which the last of the required
regulatory approvals, as contemplated by Section 5.1(b), is obtained (such date
being referred to herein as the "Valuation Date").

          (c)  If, between the date of this Agreement and the Effective Time,
the outstanding shares of RCFC Common Stock shall have been changed into a
different number of shares or into a different class by reason of any stock
dividend, subdivision, reclassification, 

                                       5
<PAGE>
 
recapitalization, split, combination or exchange of shares (each, a "Stock
Adjustment"), the Merger Consideration shall be adjusted correspondingly to the
extent appropriate to reflect the Stock Adjustment.

          (d)  As of the Effective Time, each Excluded Share, other than
Dissenters' Shares, shall be cancelled and retired and shall cease to exist, and
no exchange or payment shall be made with respect thereto.  All shares of RCFC
Common Stock and RCFC Preferred Stock (as defined in Section 2.4(b)) that are
held by Bayonne, if any, other than shares held in a fiduciary capacity or in
satisfaction of a debt previously contracted, shall become treasury stock of
RCFC.

          Section 1.3.   Exchange Procedures.
                         ------------------- 

          (a) Appropriate transmittal materials ("Letter of Transmittal") shall
be mailed as soon as reasonably practicable after the Effective Time, and in no
event later than 5 business days thereafter, to each holder of record of Bayonne
Common Stock as of the Effective Time.  A Letter of Transmittal will be deemed
properly completed only if accompanied by certificates representing all shares
of Bayonne Common Stock to be converted thereby.

          (b)  At and after the Effective Time, each certificate ("Bayonne
Certificate") previously representing shares of Bayonne Common Stock (except as
specifically set forth in Section 1.2) shall represent only the right to receive
the Merger Consideration.

          (c)  Prior to the Effective Time, RCFC shall deposit, or shall cause
to be deposited, with such bank or trust company that is selected by RCFC and is
reasonably acceptable to Bayonne to act as exchange agent ("Exchange Agent"),
for the benefit of the holders of shares of Bayonne Common Stock, for exchange
in accordance with this Section 1.3, an estimated amount of cash sufficient to
pay the aggregate amount of cash in lieu of fractional shares to be paid
pursuant to Section 1.2, and RCFC shall reserve for issuance with its Transfer
Agent and Registrar a sufficient number of shares of RCFC Common Stock to
provide for payment of the Merger Consideration. On the Closing Date, RCFC shall
have granted the Exchange Agent the requisite power and authority to effect for
and on behalf of RCFC the issuance of the number of shares of RCFC Common Stock
issuable in the share exchange.

          (d)  The Letter of Transmittal shall (i) specify that delivery shall
be effected, and risk of loss and title to the Bayonne Certificates shall pass,
only upon delivery of the Bayonne Certificates to the Exchange Agent, (ii) be in
a form and contain any other provisions as RCFC may reasonably determine and
(iii) include instructions for use in effecting the surrender of the Bayonne
Certificates in exchange for the Merger Consideration. Upon the proper surrender
of the Bayonne Certificates to the Exchange Agent, together with a properly
completed and duly executed Letter of Transmittal, the holder of such Bayonne
Certificates shall be entitled to receive in exchange therefor (m) a certificate
representing that number of whole shares of RCFC Common Stock that such holder
has the right to receive pursuant to Section 1.2 and (n) a

                                       6
<PAGE>
 
check in the amount equal to the cash in lieu of fractional shares, if any, that
such holder has the right to receive pursuant to Section 1.2 and any dividends
or other distributions to which such holder is entitled pursuant to this Section
1.3. Bayonne Certificates so surrendered shall forthwith be cancelled. As soon
as practicable, but no later than 10 business days following receipt of the
properly completed Letter of Transmittal and any necessary accompanying
documentation, the Exchange Agent shall distribute RCFC Common Stock and cash as
provided herein. The Exchange Agent shall not be entitled to vote or exercise
any rights of ownership with respect to the shares of RCFC Common Stock held by
it from time to time hereunder, except that it shall receive and hold all
dividends or other distributions paid or distributed with respect to such shares
for the account of the persons entitled thereto. If there is a transfer of
ownership of any shares of Bayonne Common Stock not registered in the transfer
records of Bayonne, the Merger Consideration shall be issued to the transferee
thereof if the Bayonne Certificates representing such Bayonne Common Stock are
presented to the Exchange Agent, accompanied by all documents required, in the
reasonable judgment of RCFC and the Exchange Agent, (x) to evidence and effect
such transfer and (y) to evidence that any applicable stock transfer taxes have
been paid.

          (e)  No dividends or other distributions declared or made after the
Effective Time with respect to RCFC Common Stock shall be remitted to any person
entitled to receive shares of RCFC Common Stock hereunder until such person
surrenders his or her Bayonne Certificates in accordance with this Section 1.3.
Upon the surrender of such person's Bayonne Certificates, such person shall be
entitled to receive any dividends or other distributions, without interest
thereon, which theretofore had become payable with respect to shares of RCFC
Common Stock represented by such person's Bayonne Certificates.

          (f)  From and after the Effective Time there shall be no transfers on
the stock transfer records of Bayonne of any shares of Bayonne Common Stock.
If, after the Effective Time, Bayonne Certificates are presented to RCFC, they
shall be cancelled and exchanged for the Merger Consideration deliverable in
respect thereof pursuant to this Agreement in accordance with the procedures set
forth in this Section 1.3.

          (g)  Any portion of the aggregate amount of cash to be paid in lieu of
fractional shares pursuant to Section 1.2, any dividends or other distributions
to be paid pursuant to this Section 1.3 or any proceeds from any investments
thereof that remains unclaimed by the stockholders of Bayonne for 6 months after
the Effective Time shall be repaid by the Exchange Agent to RCFC upon the
written request of RCFC. After such request is made, any stockholders of Bayonne
who have not theretofore complied with this Section 1.3 shall look only to RCFC
for the Merger Consideration deliverable in respect of each share of Bayonne
Common Stock such stockholder holds, as determined pursuant to Section 1.2 of
this Agreement, without any interest thereon.  If outstanding Bayonne
Certificates are not surrendered prior to the date on which such payments would
otherwise escheat to or become the property of any governmental unit or agency,
the unclaimed items shall, to the extent permitted by any abandoned property,
escheat or other applicable laws, become the property of RCFC (and, to the
extent not in its possession, 

                                       7
<PAGE>
 
shall be paid over to it), free and clear of all claims or interest of any
person previously entitled to such claims. Notwithstanding the foregoing,
neither the Exchange Agent nor any party to this Agreement (or any affiliate
thereof) shall be liable to any former holder of Bayonne Common Stock for any
amount delivered to a public official pursuant to applicable abandoned property,
escheat or similar laws.

          (h)  RCFC and the Exchange Agent shall be entitled to rely upon
Bayonne's stock transfer books to establish the identity of those persons
entitled to receive the Merger Consideration, which books shall be conclusive
with respect thereto.  In the event of a dispute with respect to ownership of
stock represented by any Bayonne Certificate, RCFC and the Exchange Agent shall
be entitled to deposit any Merger Consideration represented thereby in escrow
with an independent third party and thereafter be relieved with respect to any
claims thereto.

          (i)  If any Bayonne Certificate shall have been lost, stolen or
destroyed, upon the making of an affidavit of that fact by the person claiming
such Bayonne Certificate to be lost, stolen or destroyed and, if required by the
Exchange Agent, the posting by such person of a bond in such amount as the
Exchange Agent may direct as indemnity against any claim that may be made
against it with respect to such Bayonne Certificate, the Exchange Agent will
issue in exchange for such lost, stolen or destroyed Bayonne Certificate the
Merger Consideration deliverable in respect thereof pursuant to Section 1.2.

          Section 1.4.   Stock Options.
                         ------------- 

          (a)  At the Effective Time, by virtue of the Merger, and without any
action on the part of any holder of an option, each option to acquire shares of
Bayonne Common Stock granted pursuant to either the 1995 Stock Option Plan or
the 1998 Stock-Based Incentive Plan (a "Bayonne Option") that is then
outstanding and unexercised shall be converted into and become an option to
acquire RCFC Common Stock on the same terms and conditions as are in effect with
respect to the Bayonne Option immediately prior to the Effective Time, except
that (i) the number of shares of RCFC Common Stock subject to such Bayonne
Option shall be equal to the number of shares of Bayonne Common Stock subject to
such Bayonne Option immediately prior to the Effective Time multiplied by the
Exchange Ratio, the product being rounded, if necessary, up or down to the
nearest whole share, and (ii) the per share exercise price of the option shall
be adjusted by dividing the per share exercise price of the Bayonne Option by
the Exchange Ratio, and rounding up to the nearest cent.  It is intended that
the foregoing assumption shall be effected in a manner which is consistent with
the requirements of Section 424 of the Internal Revenue Code of 1986, as
amended, as to any Bayonne Option that is an incentive stock option.

          Section 1.5.   Bank Merger.  Concurrently with or as soon as
                         -----------                                  
practicable after the execution and delivery of this Agreement, Richmond County
Savings Bank ("RCFC Bank"), a wholly-owned subsidiary of RCFC, and First Savings
Bank of New Jersey, SLA ("First Savings"), a wholly-owned subsidiary of Bayonne,
shall enter into the Plan of Bank Merger, in 

                                       8
<PAGE>
 
the form attached hereto as Exhibit B, pursuant to which the Bank Merger will be
effected. The parties hereto intend that the Bank Merger shall become effective
on the Effective Date. The Plan of Bank Merger shall provide that the directors
of RCFC Bank as the surviving entity of the Bank Merger shall be all of the
directors of RCFC Bank serving immediately prior to the Bank Merger.

          Section 1.6.   Directors of RCFC after Effective Time.  At the
                         --------------------------------------         
Effective Time, the directors of RCFC shall consist of (a) the directors of RCFC
serving immediately prior to the Effective Time and (b) one additional person
who shall become a director of RCFC in accordance with Section 4.13.  Other than
as provided in Section 4.13, no director of Bayonne shall become a director of
RCFC.

          Section 1.7.   Alternative Structure.  Notwithstanding anything to the
                         ---------------------                                  
contrary contained in this Agreement, prior to the Effective Time, RCFC may
specify that the structure of the transactions contemplated hereby be revised
and the parties shall enter into such alternative transactions as RCFC may
determine to effect the purposes of this Agreement; provided, however, that such
revised structure shall not (i) adversely affect the treatment of the
transaction as a pooling-of-interests for accounting purposes, (ii) adversely
affect the tax effects or alter or change the amount or kind of the Merger
Consideration or the treatment of Bayonne Options or the economic benefits of
the transactions contemplated hereby to the holders of Bayonne Common Stock,
(iii) diminish the benefits to be received by the directors, officers or
employees of Bayonne or First Savings as set forth in or as contemplated by this
Agreement, and (iv) materially impede or delay the receipt of any approval
referred to in this Agreement (as defined in Section 7.1).  This Agreement and
any related documents shall be appropriately amended in order to reflect any
such revised structure.

          Section 1.8.   Certificate of Incorporation and Bylaws of the
                         ----------------------------------------------
Surviving Corporation.  The Certificate of Incorporation and Bylaws of RCFC in
- ---------------------                                                         
effect immediately prior to the Effective Time shall be the Certificate of
Incorporation and Bylaws of the surviving corporation.


                                   ARTICLE II
                         REPRESENTATIONS AND WARRANTIES
                         ------------------------------

          Section 2.1.   Disclosure Letters.  On or prior to the execution and
                         ------------------                                   
delivery of this Agreement, Bayonne and RCFC each shall have delivered to the
other a letter (each, its "Disclosure Letter") setting forth, among other
things, facts, circumstances and events the disclosure of which is required or
appropriate in relation to any or all of their respective representations and
warranties (and making specific reference to the Section of this Agreement to
which they relate), other than Section 2.3(g) and Section 2.4(g); provided, that
(a) no such fact, circumstance or event is required to be set forth in the
Disclosure Letter as an exception to a representation or warranty if its absence
is not reasonably likely to result in the related 

                                       9
<PAGE>
 
representation or warranty being deemed untrue or incorrect under the standards
established by Section 2.2 and (b) the mere inclusion of a fact, circumstance or
event in a Disclosure Letter shall not be deemed an admission by a party that
such item represents a material exception or that such item is reasonably likely
to result in a Material Adverse Effect (as defined in Section 2.2(b)).

          Section 2.2.   Standards.
                         --------- 

          (a)  No representation or warranty of Bayonne or RCFC contained in
Sections 2.3 or 2.4, respectively, shall be deemed untrue or incorrect, and no
party hereto shall be deemed to have breached a representation or warranty, on
account of the existence of any fact, circumstance or event unless, as a direct
or indirect consequence of such fact, circumstance or event, individually or
taken together with all other facts, circumstances or events inconsistent with
any paragraph of Sections 2.3 or 2.4, as applicable, there is reasonably likely
to exist a Material Adverse Effect.  Bayonne's representations, warranties and
covenants contained in this Agreement shall not be deemed to be untrue or
breached as a result of effects arising solely from actions taken in connection
with this Agreement or in compliance with a written request of RCFC.

          (b)  As used in this Agreement, the term "Material Adverse Effect"
means either (i) an effect which is material and adverse to the business,
financial condition or results of operations of Bayonne or RCFC, as the context
may dictate, and its Subsidiaries (as defined herein) taken as a whole;
provided, however, that any such effect resulting from any (A) changes in laws,
rules or regulations or generally accepted accounting principles or regulatory
accounting requirements or interpretations thereof that apply to both RCFC and
RCFC Bank and Bayonne and First Savings, as the case may be, or to similarly
situated financial and/or depository institutions or (B) changes in economic
conditions affecting financial institutions generally, including but not limited
to, changes in the general level of market interest rates shall not be
considered in determining if a Material Adverse Effect has occurred; or (ii) the
failure of (x) a representation or warranty contained in Section 2.3(a)(i) and
(iv), Section 2.3(c), Section 2.3(g)(iii), Sections 2.4(a)(i) and (iv), Section
2.4(c), Section 2.4(g)(iii) or Section 2.4(l) to be true and correct in all
material respects or (y) a representation or warranty contained in the last
sentence of each of Section 2.3(e) or Section 2.4(e), the second sentence of
each of Section 2.3(f)(i) or Section 2.4(f)(i) and the first two sentences of
each of Section 2.3(aa) or Section 2.4(x) to be true and correct in all material
respects.

          (c)  For purposes of this Agreement, "knowledge" shall mean, with
respect to a party hereto, actual knowledge of the members of the Board of
Directors of that party or any officer of that party with the title ranking not
less than senior vice president.

          Section 2.3.   Representations and Warranties of Bayonne.  Subject to
                         -----------------------------------------             
Sections 2.1 and 2.2, Bayonne represents and warrants to RCFC that, except as
disclosed in Bayonne's Disclosure Letter:

                                       10
<PAGE>
 
          (a)  Organization.  (i)   Bayonne is a corporation duly organized,
               ------------                                                 
validly existing and in good standing under the laws of the State of Delaware
and is duly registered as a savings and loan holding company under the Home
Owners' Loan Act, as amended ("HOLA") . First Savings is a stock savings
association duly organized, validly existing and in good standing under the laws
of the State of New Jersey.  Each Subsidiary (as defined below) of First Savings
is a corporation, limited liability company or partnership duly organized,
validly existing and in good standing under the laws of its jurisdiction of
incorporation or organization.  Each of Bayonne and its Subsidiaries has all
requisite corporate power and authority to own, lease and operate its properties
and to carry on its business as now being conducted.  As used in this Agreement,
unless the context requires otherwise, the term "Subsidiary" when used with
respect to any party means any corporation or other organization, whether
incorporated or unincorporated, which is consolidated with such party for
financial reporting purposes or which is controlled, directly or indirectly, by
such party.

               (ii)  Each of Bayonne and its Subsidiaries has the requisite
corporate power and authority, and is duly qualified and is in good standing, to
do business in each jurisdiction in which the nature of its business or the
ownership or leasing of its properties makes such qualification necessary.

               (iii)  Bayonne's Disclosure Letter sets forth all of Bayonne's
Subsidiaries and all entities (whether corporations, partnerships or similar
organizations), including the corresponding percentage ownership, in which
Bayonne owns, directly or indirectly, 5% or more of the ownership interests as
of the date of this Agreement and indicates for each of Bayonne's Subsidiaries,
as of such date, its jurisdiction of organization and the jurisdiction(s)
wherein it is qualified to do business. All such Subsidiaries and ownership
interests are in compliance with all applicable laws, rules and regulations
relating to direct investments in equity ownership interests.  Bayonne owns,
either directly or indirectly, all of the outstanding capital stock of each of
its Subsidiaries.  No Subsidiary of Bayonne other than First Savings is an
"insured depository institution" as defined in the Federal Deposit Insurance
Act, as amended ("FDIA"), and the applicable regulations thereunder. All of the
shares of capital stock of each of the Subsidiaries held by Bayonne or any of
its other Subsidiaries are fully paid, nonassessable and not subject to any
preemptive rights and are owned by Bayonne or a Subsidiary of Bayonne free and
clear of any claims, liens, encumbrances or restrictions (other than those
imposed by applicable federal and state securities laws), and there are no
agreements or understandings with respect to the voting or disposition of any
such shares.

               (iv)  The deposits of First Savings are insured by the Savings
Association Insurance Fund ("SAIF") of the Federal Deposit Insurance Corporation
("FDIC") to the extent provided in the FDIA.

          (b)  Capital Structure.   (i)  The authorized capital stock of Bayonne
               -----------------                                                
consists of 22,000,000 shares of Bayonne Common Stock and 2,000,000 shares of
preferred stock, par value $.01 per share ("Bayonne Preferred Stock").  As of
the date of this Agreement: 

                                       11
<PAGE>
 
(A) 9,094,495 shares of Bayonne Common Stock were issued and outstanding, (B) no
shares of Bayonne Preferred Stock were issued and outstanding, (C) no shares of
Bayonne Common Stock were reserved for issuance, except that 945,085 shares of
Bayonne Common Stock were reserved for issuance pursuant to the Bayonne Option
Plans, (D) no shares of Bayonne Preferred Stock were reserved for issuance and
(E) 194,768 shares of Bayonne Common Stock were held by Bayonne in its treasury
or by its Subsidiaries. The authorized capital stock of First Savings consists
of 20,000,000 shares of common stock, par value $.10 per share, and 10,000,000
shares of preferred stock, par value $.10 per share. As of the date of this
Agreement, 1,000 shares of such common stock were outstanding, no shares of such
preferred stock were outstanding and all outstanding shares of such common stock
were, and as of the Effective Time will be, owned by Bayonne. All outstanding
shares of capital stock of Bayonne and First Savings are duly authorized and
validly issued, fully paid and nonassessable and not subject to any preemptive
rights and, with respect to shares held by Bayonne in its treasury or by its
Subsidiaries, are free and clear of all liens, claims, encumbrances or
restrictions (other than those imposed by applicable federal and state
securities laws) and there are no agreements or understandings with respect to
the voting or disposition of any such shares. Bayonne's Disclosure Letter sets
forth a complete and accurate list of all options to purchase Bayonne Common
Stock that have been granted pursuant to the Bayonne Option Plans and all
restricted stock grants under the Bayonne RRP, including the dates of grant,
exercise prices, dates of vesting, dates of termination and shares subject to
each grant.

               (ii)  No bonds, debentures, notes or other indebtedness having
the right to vote on any matters on which stockholders may vote ("Voting Debt")
of Bayonne are issued or outstanding.

               (iii)  As of the date of this Agreement, except for this
Agreement, the Option Agreement and the Bayonne Option Plans, neither Bayonne
nor any of its Subsidiaries has or is bound by any outstanding options,
warrants, calls, rights, convertible securities, commitments or agreements of
any character obligating Bayonne or any of its Subsidiaries to issue, deliver or
sell, or cause to be issued, delivered or sold, any additional shares of capital
stock of Bayonne or any of its Subsidiaries or obligating Bayonne or any of its
Subsidiaries to grant, extend or enter into any such option, warrant, call,
right, convertible security, commitment or agreement. As of the date hereof,
there are no outstanding contractual obligations of Bayonne or any of its
Subsidiaries to repurchase, redeem or otherwise acquire any shares of capital
stock of Bayonne or any of its Subsidiaries.

          (c)  Authority.  Each of Bayonne and First Savings has all requisite
               ---------                                                      
corporate power and authority to enter into this Agreement and the Plan of Bank
Merger, respectively, and, subject to approval of this Agreement by the
requisite vote of Bayonne's stockholders and receipt of all required regulatory
or governmental approvals, as contemplated by Section 5.1(b) of this Agreement,
to consummate the transactions contemplated hereby.  The execution and delivery
of this Agreement and the Bank Plan of Merger, and, subject to the approval of
this Agreement by Bayonne's stockholders, the consummation of the transactions
contemplated hereby, have been 

                                       12
<PAGE>
 
duly authorized by all necessary corporate actions on the part of Bayonne and
First Savings. This Agreement has been duly executed and delivered by Bayonne
and constitutes a valid and binding obligation of Bayonne, enforceable in
accordance with its terms subject to applicable bankruptcy, insolvency and
similar laws affecting creditors' rights and remedies generally and subject, as
to enforceability, to general principles of equity, whether applied in a court
of law or a court of equity.

          (d)  Stockholder Approval; Fairness Opinion.  The affirmative vote 
               --------------------------------------             
of a majority of the outstanding shares of Bayonne Common Stock entitled to vote
on this Agreement is the only vote of the stockholders of Bayonne required for
approval of this Agreement and the consummation of the Merger and the related
transactions contemplated hereby. Bayonne has received the written opinion of
Sandler O'Neill & Partners, L.P. to the effect that, as of the date hereof, the
Exchange Ratio to be received by Bayonne's stockholders is fair, from a
financial point of view, to such stockholders.

          (e)  No Violations.  The execution, delivery and performance of this
               -------------                                                  
Agreement and Option Agreement by Bayonne do not, and the consummation of the
transactions contemplated hereby will not, constitute (i) assuming receipt of
all Requisite Regulatory Approvals (as defined below) and requisite stockholder
approvals, a breach or violation of, or a default under, any law, rule or
regulation or any judgment, decree, order, governmental permit or license, or
agreement, indenture or instrument of Bayonne or any of its Subsidiaries, or to
which Bayonne or any of its Subsidiaries (or any of their respective properties)
is subject, (ii) a breach or violation of, or a default under, the certificate
of incorporation or bylaws of Bayonne or the similar organizational documents of
any of its Subsidiaries or (iii) a breach or violation of, or a default under
(or an event which, with due notice or lapse of time or both, would constitute a
default under), or result in the termination of, accelerate the performance
required by, or result in the creation of any lien, pledge, security interest,
charge or other encumbrance upon any of the properties or assets of Bayonne or
any of its Subsidiaries, under, any of the terms, conditions or provisions of
any note, bond, indenture, deed of trust, loan agreement or other agreement,
instrument or obligation to which Bayonne or any of its Subsidiaries is a party,
or to which any of their respective properties or assets may be subject; and the
consummation by Bayonne and First Savings of the transactions (including the
Bank Merger) contemplated hereby (exclusive of the effect of any changes
effected pursuant to Section 1.7) will not require any approval, consent or
waiver under any such law, rule, regulation, judgment, decree, order,
governmental permit or license or the approval, consent or waiver of any other
party to any such agreement, indenture or instrument, other than (x) the
approval of the holders of a majority of the outstanding shares of Bayonne
Common Stock entitled to vote, (y)  the approval of the Office of Thrift
Supervision ("OTS") under HOLA, and (z) the approval of the New Jersey
Department of Banking (the "NJBD") and the approval of the appropriate
regulatory authority under Section 18(c) of the FDIA.  As of the date hereof,
the executive officers of Bayonne know of no reason pertaining to Bayonne why
any of the approvals referred to in this Section 2.3(e) should not be obtained
without the imposition of any material condition or restriction described in the
proviso to Section 5.1(b).

                                       13
<PAGE>
 
          (f)  Reports.  (i)  As of their respective dates, none of the reports
               -------                                                         
or other statements filed by Bayonne or First Savings on or subsequent to March
31, 1998 with the FDIC or the Securities and Exchange Commission ("SEC")
(collectively, "Bayonne's Reports"), contained, or will contain, any untrue
statement of a material fact or omitted or will omit to state a material fact
required to be stated therein or necessary to make the statements made therein,
in light of the circumstances under which they were made, not misleading.  Each
of the financial statements of Bayonne included in Bayonne's Reports complied as
to form, as of their respective dates of filing with the SEC, in all material
respects with applicable accounting requirements and with the published rules
and regulations of the SEC with respect thereto and have been prepared in
accordance with generally accepted accounting principles applied on a consistent
basis during the periods involved ("GAAP")(except as may be indicated in the
notes thereto or, in the case of the unaudited financial statements, as
permitted by the SEC).  Each of the consolidated statements of condition
contained or incorporated by reference in Bayonne's Reports (including in each
case any related notes and schedules) and each of the consolidated statements of
operations, consolidated statements of cash flows and consolidated statements of
changes in stockholders' equity, contained or incorporated by reference in
Bayonne's Reports (including in each case any related notes and schedules)
fairly presented, or will fairly present, as the case may be (A) the financial
position of the entity or entities to which it relates as of its date, and (B)
the results of operations, stockholders' equity and cash flows, as the case may
be, of the entity or entities to which it relates for the periods set forth
therein (subject, in the case of unaudited interim statements, to normal year-
end audit adjustments that are not material in amount or effect), in each case
in accordance with GAAP, except as may be noted therein.  Bayonne has made
available to RCFC a true and complete copy of each of Bayonne's Reports filed
with the SEC since March 31, 1998.

               (ii)  Bayonne and each of its Subsidiaries have each timely filed
all material reports, registrations and statements, together with any amendments
required to be made with respect thereto, that they were required to file since
March 31, 1995 with (A) the NJBD, (B) the FDIC, (C) the OTS, (D) the National
Association of Securities Dealers, Inc. ("NASD"), (E) the SEC and (F) any other
self-regulatory organization ("SRO"), and, to Bayonne's knowledge, have paid all
fees and assessments due and payable in connection therewith.

          (g)  Absence of Certain Changes or Events.  Except as disclosed in
               ------------------------------------                         
Bayonne's Reports filed on or prior to the date of this Agreement, since March
31, 1998, (i) Bayonne and its Subsidiaries have not incurred any liability,
except in the ordinary course of their business consistent with past practice,
(ii) Bayonne and its Subsidiaries have conducted their respective businesses
only in the ordinary and usual course of such businesses and (iii) there has not
been any Material Adverse Effect with respect to Bayonne.

          (h)  Absence of Claims.  Except as set forth in Bayonne's Disclosure
               -----------------                                              
Letter, no litigation, proceeding, controversy, claim or action before any court
or governmental agency is pending against Bayonne or any of its Subsidiaries
and, to the best of Bayonne's knowledge, no such litigation, proceeding,
controversy, claim or action has been threatened.

                                       14
<PAGE>
 
          (i)  Absence of Regulatory Actions.  Neither Bayonne nor any of its
               -----------------------------                                 
Subsidiaries is a party to any cease and desist order, written agreement or
memorandum of understanding with, or any commitment letter or similar
undertaking to, or is subject to any action, proceeding, order or directive by,
or is a recipient of any extraordinary supervisory letter from any federal or
state governmental authority charged with the supervision or regulation of
depository institutions or depository institution holding companies or engaged
in the insurance of bank and/or savings and loan deposits ("Government
Regulators"), or has adopted any board resolutions at the request of any
Government Regulator, nor has it been advised by any Government Regulator that
it is contemplating issuing or requesting (or is considering the appropriateness
of issuing or requesting) any such action, proceeding, order, directive, written
agreement, memorandum of understanding, extraordinary supervisory letter,
commitment letter, board resolutions or similar undertaking.

          (j)  Taxes.  All federal, state, local and foreign tax returns 
               -----         
required to be filed by or on behalf of Bayonne or any of its Subsidiaries have
been timely filed or requests for extensions have been timely filed and any such
extension shall have been granted and not have expired, and all such filed
returns are complete and accurate in all material respects. All taxes shown on
such returns, all taxes required to be shown on returns for which extensions
have been granted and all other taxes required to be paid by Bayonne or any of
its Subsidiaries have been paid in full or adequate provision has been made for
any such taxes on Bayonne's balance sheet (in accordance with GAAP). For
purposes of this Section 2.3(j), the term "taxes" shall include all income,
franchise, gross receipts, real and personal property, real property transfer
and gains, wage and employment taxes. As of the date of this Agreement, there is
no audit examination, deficiency assessment, tax investigation or refund
litigation with respect to any taxes of Bayonne or any of its Subsidiaries, and
no claim has been made by any authority in a jurisdiction where Bayonne or any
of its Subsidiaries do not file tax returns that Bayonne or any such Subsidiary
is subject to taxation in that jurisdiction. All taxes, interest, additions and
penalties due with respect to completed and settled examinations or concluded
litigation relating to Bayonne or any of its Subsidiaries have been paid in full
or adequate provision has been made for any such taxes on Bayonne's balance
sheet (in accordance with GAAP). Bayonne and its Subsidiaries have not executed
an extension or waiver of any statute of limitations on the assessment or
collection of any material tax due that is currently in effect. Bayonne and each
of its Subsidiaries has withheld and paid all taxes required to have been
withheld and paid in connection with amounts paid or owing to any employee,
independent contractor, creditor, stockholder or other third party, and Bayonne
and each of its Subsidiaries has timely complied with all applicable information
reporting requirements under Part III, Subchapter A of Chapter 61 of the Code
and similar applicable state and local information reporting requirements.
Neither Bayonne nor any of its Subsidiaries (i) has made an election under
Section 341(f) of the Code, (ii) has issued or assumed any obligation under
Section 279 of the Code, any high yield discount obligation as described in
Section 163(i) of the Code or any registration-required obligation within the
meaning of Section 163(f)(2) of the Code that is not in registered form or (iii)
is or has been a United States real property holding corporation within the
meaning of Section 897(c)(2) of the Code.

                                       15
<PAGE>
 
          (k)  Agreements.  (i)  Except for the Option Agreement and
               ----------                                                
arrangements made in the ordinary course of business, and except as set forth in
Bayonne's Disclosure Letter, Bayonne and its Subsidiaries are not bound by any
material contract (as defined in Item 601(b)(10) of Regulation S-K) to be
performed after the date hereof that has not been filed with or incorporated by
reference in Bayonne's Report.  Except as disclosed in Bayonne's Disclosure
Letter, neither Bayonne nor any of its Subsidiaries is a party to an oral or
written (A) consulting agreement (other than data processing, software
programming and licensing contracts entered into in the ordinary course of
business) not terminable on 60 days' or less notice, (B) agreement with any
executive officer or other key employee of Bayonne or any of its Subsidiaries
the benefits of which are contingent, or the terms of which are materially
altered, upon the occurrence of a transaction involving Bayonne or any of its
Subsidiaries of the nature contemplated by this Agreement or the Option
Agreement, (C) agreement with respect to any employee or director of Bayonne or
any of its Subsidiaries providing any term of employment or compensation
guarantee extending for a period longer than 60 days or for the payment of in
excess of $30,000 per annum, (D) agreement or plan, including any stock option
plan, phantom stock or stock appreciation rights plan, restricted stock plan or
stock purchase plan, any of the benefits of which will be increased, or the
vesting or payment of the benefits of which will be accelerated, by the
occurrence of any of the transactions contemplated by this Agreement or the
Option Agreement or the value of any of the benefits of which will be calculated
on the basis of any of the transactions contemplated by this Agreement or the
Option Agreement or (E) agreement containing covenants that limit the ability of
Bayonne or any of its Subsidiaries to compete in any line of business or with
any person, or that involve any restriction on the geographic area in which, or
method by which, Bayonne (including any successor thereof) or any of its
Subsidiaries may carry on its business (other than as may be required by law or
any regulatory agency).

               (ii)  Neither Bayonne nor any of its Subsidiaries is in default
under or in violation of any provision of any note, bond, indenture, mortgage,
deed of trust, loan agreement, lease or other agreement to which it is a party
or by which it is bound or to which any of its respective properties or assets
is subject.

               (iii)  Bayonne and each of its Subsidiaries owns or possesses
valid and binding licenses and other rights to use without payment all patents,
copyrights, trade secrets, trade names, servicemarks and trademarks used in its
businesses, and neither Bayonne nor any of its Subsidiaries has received any
notice of conflict with respect thereto that asserts the right of others.  Each
of Bayonne and its Subsidiaries has performed all the obligations required to be
performed by it and are not in default under any contact, agreement, arrangement
or commitment relating to any of the foregoing.

          (l)  Labor Matters.  Neither Bayonne nor any of its Subsidiaries is or
               -------------                                                    
has ever been a party to, or is or has ever been bound by, any collective
bargaining agreement, contract or other agreement or understanding with a labor
union or labor organization with respect to its employees, nor is Bayonne or any
of its Subsidiaries the subject of any proceeding asserting that 

                                       16
<PAGE>
 
it has committed an unfair labor practice or seeking to compel it or any such
Subsidiary to bargain with any labor organization as to wages and conditions of
employment, nor is there any strike, other labor dispute or organizational
effort involving Bayonne or any of its Subsidiaries pending or, to Bayonne's
knowledge, threatened. Bayonne and its Subsidiaries are in compliance with
applicable laws regarding employment of employees and retention of independent
contractors and are in compliance with applicable employment tax laws.

          (m)  Employee Benefit Plans.  Bayonne's Disclosure Letter contains a
               ----------------------                                         
complete and accurate list of all pension, retirement, stock option, stock
purchase, stock ownership, savings, stock appreciation right, profit sharing,
deferred compensation, consulting, bonus, group insurance, severance and other
benefit plans, contracts, agreements and arrangements, including, but not
limited to, "employee benefit plans," as defined in Section 3(3) of the Employee
Retirement Income Security Act of 1974, as amended ("ERISA"), incentive and
welfare policies, contracts, plans and arrangements and all trust agreements
related thereto with respect to any present or former directors, officers or
other employees of Bayonne or any of its Subsidiaries (hereinafter collectively
referred to as the "Bayonne Employee Plans").  All of the Bayonne Employee Plans
comply in all material respects with all applicable requirements of ERISA, the
Code and other applicable laws; there has occurred no "prohibited transaction"
(as defined in Section 406 of ERISA or Section 4975 of the Code) which is likely
to result in the imposition of any penalties or taxes under Section 502(i) of
ERISA or Section 4975 of the Code upon Bayonne or any of its Subsidiaries.
Neither Bayonne nor any of its Subsidiaries has provided, or is required to
provide, security to any Bayonne Pension Plan or to any single-employer plan of
an ERISA Affiliate pursuant to Section 401(a)(29) of the Code.  Neither Bayonne,
its Subsidiaries, nor any ERISA Affiliate has contributed to any "multiemployer
plan," as defined in Section 3(37) of ERISA, on or after September 26, 1980.
Each Bayonne Employee Plan that is an "employee pension benefit plan" (as
defined in Section 3(2) of ERISA) and which is intended to be qualified under
Section 401(a) of the Code (a "Bayonne Qualified Plan") has received a favorable
determination letter from the Internal Revenue Service ("IRS"), and Bayonne and
its Subsidiaries are not aware of any circumstances likely to result in
revocation of any such favorable determination letter.  There is no pending or,
to Bayonne's knowledge, threatened litigation, administrative action or
proceeding relating to any Bayonne Employee Plan.  There has been no
announcement or commitment by Bayonne or any of its Subsidiaries to create an
additional Bayonne Employee Plan, or to amend any Bayonne Employee Plan, except
for amendments required by applicable law which do not materially increase the
cost of such Bayonne Employee Plan; and, except as specifically identified in
Bayonne's Disclosure Letter, Bayonne and its Subsidiaries do not have any
obligations for post-retirement or post-employment benefits under any Bayonne
Employee Plan that cannot be amended or terminated upon 60 days' notice or less
without incurring any liability thereunder, except for coverage required by Part
6 of Title I of ERISA or Section 4980B of the Code, or similar state laws, the
cost of which is borne by the insured individuals.  With respect to Bayonne or
any of its Subsidiaries, for the Employee Plans listed in Bayonne's Disclosure
Letter, the execution and delivery of this Agreement and the consummation of the
transactions contemplated hereby will not result in any payment or series of
payments by Bayonne or any of its Subsidiaries to any person which is an "excess
parachute 

                                       17
<PAGE>
 
payment" (as defined in Section 280G of the Code), increase or secure (by way of
a trust or other vehicle) any benefits payable under any Bayonne Employee Plan
or accelerate the time of payment or vesting of any such benefit. With respect
to each Bayonne Employee Plan, Bayonne has supplied to RCFC a true and correct
copy of (A) the annual report on the applicable form of the Form 5500 series
filed with the IRS for the most recent three plan years, if required to be
filed, (B) such Bayonne Employee Plan, including amendments thereto, (C) each
trust agreement, insurance contract or other funding arrangement relating to
such Bayonne Employee Plan, including amendments thereto, (D) the most recent
summary plan description and summary of material modifications thereto for such
Bayonne Employee Plan, if the Bayonne Employee Plan is subject to Title I of
ERISA, and (E) the most recent determination letter issued by the IRS if such
Employee Plan is a Qualified Plan.

          (n)  Title to Assets.  Bayonne and each of its Subsidiaries has good
               ---------------                                                
and marketable title to its properties and assets (including any intellectual
property asset such as any trademark, service mark, tradename or copyright) and
property acquired in a judicial foreclosure proceeding or by way of a deed in
lieu of foreclosure or similar transfer, other than property as to which it is
lessee, in which case the related lease is valid and in full force and effect.
Each lease pursuant to which Bayonne or any of its Subsidiaries is lessor is
valid and in full force and effect and no lessee under any such lease is in
default or in violation of any provisions of any such lease.  All material
tangible properties of Bayonne and each of its Subsidiaries are in a good state
of maintenance and repair, conform with all applicable ordinances, regulations
and zoning laws and are considered by Bayonne to be adequate for the current
business of Bayonne and its Subsidiaries.

          (o)  Compliance with Laws.  Bayonne and each of its Subsidiaries has
               --------------------                                           
all permits, licenses, certificates of authority, orders and approvals of, and
has made all filings, applications and registrations with, all federal, state,
local and foreign governmental or regulatory bodies that are required in order
to permit it to carry on its business as it is presently conducted; all such
permits, licenses, certificates of authority, orders and approvals are in full
force and effect, and, to the best knowledge of Bayonne, no suspension or
cancellation of any of them is threatened. Since the date of its incorporation,
the corporate affairs of Bayonne have not been conducted in violation of any
law, ordinance, regulation, order, writ, rule, decree or approval of any federal
or state regulatory authority having jurisdiction over insured depositary
institutions or their holding companies, the SEC, the NASD or any other SRO
(each, a "Governmental Entity").  The businesses of Bayonne and its Subsidiaries
are not being conducted in violation of any law, ordinance, regulation, order,
writ, rule,  decree or condition to approval of any Governmental Entity.

          (p)  Fees.  Other than financial advisory services performed for
               ----                                                       
Bayonne by Sandler O'Neill & Partners, L.P., neither Bayonne nor any of its
Subsidiaries, nor any of their respective officers, directors, employees or
agents, has employed any broker or finder or incurred any liability for any
financial advisory fees, brokerage fees, commissions or finder's fees, and no

                                       18
<PAGE>
 
broker or finder has acted directly or indirectly for Bayonne or any of its
Subsidiaries in connection with this Agreement or the transactions contemplated
hereby.

          (q)  Environmental Matters.  (i)  With respect to Bayonne and each
               ---------------------                                          
of its Subsidiaries:

               (A)  Each of Bayonne and its Subsidiaries, the Participation
Facilities (as defined herein), and, to Bayonne's knowledge, the Loan Properties
(as defined herein) are, and have been, in substantial compliance with, and are
not liable under, all Environmental Laws (as defined herein);

               (B)  There is no suit, claim, action, demand, executive or
administrative order, directive, investigation or proceeding pending or, to
Bayonne's knowledge, threatened, before any court, governmental agency or board
or other forum against it or any of its Subsidiaries or any Participation
Facility (x) for alleged noncompliance (including by any predecessor) with, or
liability under, any Environmental Law or (y) relating to the presence of or
release (as defined herein) into the environment of any Hazardous Material (as
defined herein), whether or not occurring at or on a site owned, leased or
operated by it or any of its Subsidiaries or any Participation Facility;

               (C)  To Bayonne's knowledge, there is no suit, claim, action,
demand, executive or administrative order, directive, investigation or
proceeding pending or threatened before any court, governmental agency or board
or other forum relating to or against any Loan Property (or Bayonne or any of
its Subsidiaries in respect of such Loan Property) (x) relating to alleged
noncompliance (including by any predecessor) with, or liability under, any
Environmental Law or (y) relating to the presence of or release into the
environment of any Hazardous Material, whether or not occurring at or on a site
owned, leased or operated by a Loan Property;

               (D)  To Bayonne's knowledge, the properties currently owned or
operated by Bayonne or any of its Subsidiaries (including, without limitation,
soil, groundwater or surface water on, under or adjacent to the properties, and
buildings thereon) are not contaminated with and do not otherwise contain any
Hazardous Material other than as permitted under applicable Environmental Law;

               (E)  Neither Bayonne nor any of its Subsidiaries has received any
notice, demand letter, executive or administrative order, directive or request
for information from any federal, state, local or foreign governmental entity or
any third party indicating that it may be in violation of, or liable under, any
Environmental Law;

               (F)  To Bayonne's knowledge, there are no underground storage
tanks on, in or under any properties owned or operated by Bayonne or any of its
Subsidiaries or any Participation Facility and no underground storage tanks have
been closed or removed from any 

                                       19
<PAGE>
 
properties owned or operated by Bayonne or any of its Subsidiaries or any
Participation Facility; and

               (G)  To Bayonne's knowledge, during the period of (l) Bayonne's
or any of its Subsidiaries' ownership or operation of any of their respective
current properties or (m) Bayonne's or any of its Subsidiaries' participation in
the management of any Participation Facility, there has been no contamination by
or release of Hazardous Materials in, on, under or affecting such properties. To
Bayonne's knowledge, prior to the period of (x) Bayonne's or any of its
Subsidiaries' ownership or operation of any of their respective current
properties or (y) Bayonne's or any of its Subsidiaries' participation in the
management of any Participation Facility, there was no contamination by or
release of Hazardous Material in, on, under or affecting such properties.

               (ii)  The following definitions apply for purposes of this
Section 2.3(r) and Section 2.4(r): (w) "Loan Property" means any property in
which the applicable party (or a Subsidiary of it) holds a security interest,
and, where required by the context, includes the owner or operator of such
property, but only with respect to such property; (x) "Participation Facility"
means any facility in which the applicable party (or a Subsidiary of it)
participates in the management (including all property held as trustee or in any
other fiduciary capacity) and, where required by the context, includes the owner
or operator of such property, but only with respect to such property; (y)
"Environmental Law" means (i) any federal, state or local law, statute,
ordinance, rule, regulation, code, license, permit, authorization, approval,
consent, legal doctrine, order, directive, executive or administrative order,
judgment, decree, injunction, legal requirement or agreement with any
governmental entity relating to (A) the protection, preservation or restoration
of the environment (which includes, without limitation, air, water vapor,
surface water, groundwater, drinking water supply, structures, soil, surface
land, subsurface land, plant and animal life or any other natural resource), or
to human health or safety as it relates to Hazardous Materials, or (B) the
exposure to, or the use, storage, recycling, treatment, generation,
transportation, processing, handling, labeling, production, release or disposal
of, Hazardous Materials, in each case as amended and as now in effect. The term
Environmental Law includes all federal, state and local laws, rules, regulations
or requirements relating to the protection of the environment or health and
safety, including, without limitation, (i) the Federal Comprehensive
Environmental Response, Compensation and Liability Act of 1980, the Superfund
Amendments and Reauthorization Act of 1986, the Federal Water Pollution Control
Act of 1972, the Federal Clean Air Act, the Federal Clean Water Act, the Federal
Resource Conservation and Recovery Act of 1976 (including, but not limited to,
the Hazardous and Solid Waste Amendments thereto and Subtitle I relating to
underground storage tanks), the Federal Solid Waste Disposal and the Federal
Toxic Substances Control Act, the Federal Insecticide, Fungicide and Rodenticide
Act, the Federal Occupational Safety and Health Act of 1970 as it relates to
Hazardous Materials, the Federal Hazardous Substances Transportation Act, the
Emergency Planning and Community Right-To-Know Act, the Safe Drinking Water Act,
the Endangered Species Act, the National Environmental Policy Act, the Rivers
and Harbors Appropriation Act or any so-called "Superfund" or "Superlien" law,
each as amended and as now 

                                       20
<PAGE>
 
or hereafter in effect, and (ii) any common law or equitable doctrine
(including, without limitation, injunctive relief and tort doctrines such as
negligence, nuisance, trespass and strict liability) that may impose liability
or obligations for injuries or damages due to, or threatened as a result of, the
presence of or exposure to any Hazardous Material; and (z) "Hazardous Material"
means any substance (whether solid, liquid or gas) which is or could be
detrimental to human health or safety or to the environment, currently or
hereafter listed, defined, designated or classified as hazardous, toxic,
radioactive or dangerous, or otherwise regulated, under any Environmental Law,
whether by type or by quantity, including any substance containing any such
substance as a component. Hazardous Material includes, without limitation, any
toxic waste, pollutant, contaminant, hazardous substance, toxic substance,
hazardous waste, special waste, industrial substance, oil or petroleum, or any
derivative or by-product thereof, radon, radioactive material, asbestos,
asbestos-containing material, urea formaldehyde foam insulation, lead and
polychlorinated biphenyl.

          (r)  Loan Portfolio; Allowance; Asset Quality.  (i)  With respect to
               ----------------------------------------                         
each loan owned by Bayonne or its Subsidiaries in whole or in part (each, a
"Loan"), to Bayonne's knowledge:

               (A)  the note and the related security documents are each legal,
valid and binding obligations of the maker or obligor thereof, enforceable
against such maker or obligor in accordance with their terms;

               (B)  neither Bayonne nor any of its Subsidiaries, nor any prior
holder of a Loan, has modified the note or any of the related security documents
in any material respect or satisfied, canceled or subordinated the note or any
of the related security documents except as otherwise disclosed by documents in
the applicable Loan file;

               (C)  Bayonne or a Subsidiary is the sole holder of legal and
beneficial title to each Loan (or Bayonne's applicable participation interest,
as applicable), except as otherwise referenced on the books and records of
Bayonne;

               (D)  the note and the related security documents, copies of which
are included in the Loan files, are true and correct copies of the documents
they purport to be and have not been suspended, amended, modified, canceled or
otherwise changed except as otherwise disclosed by documents in the applicable
Loan file;

               (E)  there is no pending or threatened condemnation proceeding or
similar proceeding affecting the property that serves as security for a Loan,
except as otherwise referenced on the books and records of Bayonne;

               (F)  there is no litigation or proceeding pending or threatened
relating to the property that serves as security for a Loan that would have a
Material Adverse Effect upon the related Loan; and

                                       21
<PAGE>
 
               (G)  with respect to a Loan held in the form of a participation,
the participation documentation is legal, valid, binding and enforceable.

               (ii)  The allowance for possible losses reflected in Bayonne's
audited statement of condition at March 31, 1998 was, and the allowance for
possible losses shown on the balance sheets in Bayonne's Reports for periods
ending after December 31, 1997 will, in the opinion of management, be adequate,
as of the dates thereof, under generally accepted accounting principles
applicable to stock savings associations consistently applied.

               (iii)  Bayonne's Disclosure Letter sets forth by category the
amounts of all loans, leases, advances, credit enhancements, other extensions of
credit, commitments and interest-bearing assets of Bayonne and its Subsidiaries
that have been classified (whether regulatory or internal) as "Special Mention,"
"Substandard," "Doubtful," "Loss" or words of similar import, and Bayonne and
its Subsidiaries shall promptly after the end of any month inform RCFC of any
such classification arrived at any time after the date hereof.  The other real
estate owned ("OREO")  or words of similar import included in any non-performing
assets of Bayonne or any of its Subsidiaries is carried net of reserves at the
lower of cost or fair value, less estimated selling costs, based on current
independent appraisals or evaluations or current management appraisals or
evaluations; provided, however, that "current" shall mean within the past 12
months.

          (s)  Deposits.   None of the deposits of Bayonne or any of its
               --------                                                 
Subsidiaries is a "brokered" deposit, except as disclosed in Bayonne's
Disclosure Letter.

          (t)  Accounting Matters.  Neither Bayonne nor any of its Subsidiaries
               ------------------                                              
or, to the best of Bayonne's knowledge, any of its other affiliates has, through
the date hereof, taken or agreed to take any action that would prevent RCFC from
accounting for the business combination contemplated herein as a pooling-of-
interests, and Bayonne has no knowledge of any fact or circumstance relating to
it that would prevent such accounting treatment.

          (u)  Antitakeover Provisions Inapplicable.   Bayonne and its
               ------------------------------------                   
Subsidiaries have taken all actions required to exempt Bayonne, the Agreement,
the Merger and the Option Agreement from any provisions of an antitakeover
nature in their organization certificates and bylaws, and the provisions of any
federal or state "antitakeover," "fair price," "moratorium," "control share
acquisition" or similar laws or regulations.

          (v)  Material Interests of Certain Persons.   Except as disclosed in
               -------------------------------------                          
Bayonne's Disclosure Letter, no officer or director of Bayonne, or any
"associate" (as such term is defined in Rule 12b-2 under the Securities Exchange
Act of 1934, as amended ("Exchange Act")) of any such officer or director, has
any material interest in any material contract or property (real or personal),
tangible or intangible, used in or pertaining to the business of Bayonne or any
of its Subsidiaries.  No such interest has been created or modified since the
date of completion of the last regulatory examination of Bayonne or its
Subsidiaries.

                                       22
<PAGE>
 
          (w)  Insurance.  In the opinion of management, Bayonne and its
               ---------                                               
Subsidiaries are presently insured, and since December 31, 1995, have been
insured, for amounts deemed reasonable by management with, to Bayonne's
knowledge, financially sound insurance companies, against such risks as
companies engaged in a similar business would, in accordance with good business
practice, customarily be insured.  All of the insurance policies and bonds
maintained by Bayonne and its Subsidiaries are in full force and effect, Bayonne
and its Subsidiaries are not in default thereunder and all material claims
thereunder have been filed in due and timely fashion.

          (x)  Investment Securities; Borrowings.  (i)  Except for investments 
               ---------------------------------                                
in Federal Home Loan Bank ("FHLB") Stock, pledges to secure FHLB borrowings, and
reverse repurchase agreements entered into in arms-length transactions pursuant
to normal commercial terms and conditions and entered into in the ordinary
course of business and restrictions that exist for securities to be classified
as "held to maturity," none of the investments reflected in the consolidated
balance sheet of Bayonne for the year ended March 31, 1998, and none of the
investment securities held by it or any of its Subsidiaries since March 31,
1998, is subject to any restriction (contractual or statutory) that would
materially impair the ability of the entity holding such investment freely to
dispose of such investment at any time.

               (ii)  Except as set forth in Bayonne's Disclosure Letter, Bayonne
nor any Subsidiary is a party to or has agreed to enter into an exchange-traded
or over-the-counter equity, interest rate, foreign exchange or other swap,
forward, future, option, cap, floor or collar or any other contract that is a
derivative contract (including various combinations thereof) (each, a
"Derivatives Contract") or owns securities that (A) are referred to generically
as "structured notes," "high risk mortgage derivatives," "capped floating rate
notes" or "capped floating rate mortgage derivatives" or (B) are likely to have
changes in value as a result of interest or exchange rate changes that
significantly exceed normal changes in value attributable to interest or
exchange rate changes.

               (iii)  Set forth in Bayonne's Disclosure Letter is a true and
complete list of Bayonne's borrowed funds (excluding deposit accounts) as of the
date hereof.

          (y)  Indemnification.  Except as provided in Bayonne's Employment
               ---------------                                             
Agreements or the organization certificate or bylaws of Bayonne and its
Subsidiaries, neither Bayonne nor any Subsidiary is a party to any
indemnification agreement with any of its present or future directors, officers,
employees, agents or other persons who serve or served in any other capacity
with any other enterprise at the request of Bayonne (a "Covered Person"), and,
to the best knowledge of Bayonne, there are no claims for which any Covered
Person would be entitled to indemnification under the organization certificate
or bylaws of Bayonne or any of its Subsidiaries, under any applicable law or
regulation or under any indemnification agreement.

                                       23
<PAGE>
 
          (z)  Books and Records.  The books and records of Bayonne and its
               -----------------                                           
Subsidiaries on a consolidated basis have been, and are being, maintained in
accordance with applicable legal and accounting requirements and reflect in all
material respects the substance of events and transactions that should be
included therein.

          (aa) Corporate Documents.  Bayonne has delivered to RCFC true and
               -------------------                                         
complete copies of its certificate of incorporation and bylaws and of First
Savings's organization certificate and bylaws.  The minute books of Bayonne and
First Savings constitute a complete and correct record of all actions taken by
their respective boards of directors (and each committee thereof) and their
stockholders.  The minute books of each of Bayonne's Subsidiaries constitutes a
complete and correct record of all actions taken by the respective boards of
directors (and each committee thereof) and the stockholders of each such
Subsidiary.

          (bb) Tax Treatment of the Merger.  As of the date hereof, Bayonne has
               ---------------------------                                     
no knowledge of any fact or circumstance relating to it that would prevent the
transactions contemplated by this Agreement from qualifying as a tax-free
reorganization under the Code.

          (cc) Beneficial Ownership of RCFC Common Stock.  As of the date
               -----------------------------------------                 
hereof, Bayonne beneficially owns no shares of RCFC Common Stock and does not
have any option, warrant or right of any kind to acquire the beneficial
ownership of any shares of RCFC Common Stock.

          (dd) Year 2000 Matters.  Bayonne has completed a review of its
               -----------------                                        
computer systems to identify systems that could be affected by the "Year 2000"
issue and reasonably believes it has identified all such Year 2000 problems.
Bayonne's management has developed and commenced implementation of a plan which
is designed to complete any required initial changes to its computer systems and
to complete testing of those changes by December 31, 1998. Between the date of
this Agreement and the Effective Time, Bayonne shall use commercially
practicable efforts to implement and/or continue to undertake such plan.  Year
2000 issues have not had, and are not reasonably expected to have, a Material
Adverse Effect on Bayonne and its Subsidiaries, taken as a whole.

          (ee) Registration Statement.  The information regarding Bayonne to be
               ----------------------                                          
supplied by Bayonne for inclusion in (i) the Registration Statement on Form S-4
and/or such other form(s) as may be appropriate to be filed under the Securities
Act of 1933, as amended ("Securities Act"), with the SEC by RCFC for the purpose
of, among other things, registering the RCFC Common Stock to be issued to
Bayonne's stockholders in the Merger (as amended or supplemented from time to
time, the "Registration Statement"), or (ii) the proxy statement to be filed
with the SEC by RCFC and Bayonne under the Exchange Act and distributed in
connection with Bayonne's meeting of stockholders and RCFC's meeting of
stockholders to vote upon this Agreement (as amended or supplemented from time
to time, the "Proxy Statement," and together with the prospectus included in the
Registration Statement, as amended or supplemented from time to time, the "Proxy
Statement-Prospectus") will not, at the time such Registration Statement 

                                       24
<PAGE>
 
becomes effective, contain any untrue statement of a material fact or omit to
state any material fact required to be stated therein or necessary in order to
make the statements therein, in light of the circumstances under which they are
made, not misleading.

          (ff) Community Reinvestment Act ("CRA") Compliance.  First Savings is
               ---------------------------------------------                   
in material compliance with the applicable provisions of the CRA and the
regulations promulgated thereunder, and First Savings currently has a CRA rating
of satisfactory or better.  To Bayonne's knowledge, there is no fact or
circumstance or set of facts or circumstances that would cause First Savings to
fail to comply with such provisions or cause the CRA rating of First Savings to
fall below satisfactory.

          Section 2.4.   Representations and Warranties of RCFC.  Subject to
                         --------------------------------------             
Sections 2.1 and 2.2, RCFC represents and warrants to Bayonne that, except as
specifically disclosed in RCFC's Disclosure Letter:

          (a)  Organization.  (i)   RCFC is a corporation duly organized,
               ------------                                              
validly existing and in good standing under the laws of the State of Delaware
and is duly registered as a savings and loan holding company under HOLA.  RCFC
Bank is a stock savings bank duly organized, validly existing and in good
standing under the laws of the State of New York.  Each Subsidiary of RCFC Bank
is a corporation, limited liability company or partnership duly organized,
validly existing and in good standing under the laws of its jurisdiction of
incorporation or organization.  Each of RCFC and its Subsidiaries has all
requisite corporate power and authority to own, lease and operate its properties
and to carry on its business as now being conducted.

               (ii)  RCFC and each of its Subsidiaries has the requisite
corporate power and authority, and is duly qualified and is in good standing, to
do business in each jurisdiction in which the nature of its business or the
ownership or leasing of its properties makes such qualification necessary.

               (iii)  RCFC's Disclosure Letter sets forth all of RCFC's
Subsidiaries and all entities (whether corporations, partnerships or similar
organizations), including the corresponding percentage ownership, in which RCFC
owns, directly or indirectly, 5% or more of the ownership interests as of the
date of this Agreement and indicates for each of RCFC's Subsidiaries, as of such
date, its jurisdiction of organization and the jurisdiction(s) wherein it is
qualified to do business.  All such Subsidiaries and ownership interests are in
compliance with all applicable laws, rules and regulations relating to direct
investments in equity ownership interests.  RCFC owns, either directly or
indirectly, all of the outstanding capital stock of each of its Subsidiaries.
No Subsidiary of RCFC other than RCFC Bank is an "insured depository
institution" as defined in the FDIA and the applicable regulations thereunder.
All of the shares of capital stock of each of the Subsidiaries held by RCFC or
any of its other Subsidiaries are fully paid, nonassessable and not subject to
any preemptive rights and are owned by RCFC or a Subsidiary of RCFC free and
clear of any claims, liens, encumbrances or restrictions (other than 

                                       25
<PAGE>
 
those imposed by applicable federal and state securities laws) and there are no
agreements or understandings with respect to the voting or disposition of any
such shares.

               (iv)  The deposits of RCFC Bank are insured by the Bank Insurance
Fund ("BIF") of the FDIC and the SAIF of the FDIC to the extent provided in the
FDIA.

          (b)  Capital Structure.  (i)  The authorized capital stock of RCFC
               -----------------                                            
consists of 75,000,000 shares of RCFC Common Stock and 5,000,000 shares of
preferred stock, par value $.01 per share ("RCFC Preferred Stock").  As of the
date of this Agreement, (A) 26,423,600 shares of RCFC Common Stock were issued
and outstanding, (B) no shares of RCFC Preferred Stock were outstanding, (C) no
shares of RCFC Common Stock were reserved for issuance, except that 2,642,360
shares of RCFC Common Stock were reserved for issuance pursuant to the RCFC 1998
Stock-Based Incentive Plan and (D) no shares of RCFC Common Stock were held by
RCFC in its treasury or by its Subsidiaries.  The authorized capital stock of
RCFC Bank consists of 75,000,000 shares of common stock, par value $.01 per
share, and 5,000,000 shares of preferred stock, par value $.01 per share.  As of
the date of this Agreement, 1,000 shares of such common stock were outstanding,
no shares of such preferred stock were outstanding and all outstanding shares of
such common stock were, and as of the Effective Time will be, owned by RCFC.
All outstanding shares of capital stock of RCFC and RCFC Bank are validly
issued, fully paid and nonassessable and not subject to any preemptive rights
and, with respect to shares held by RCFC in its treasury or by its Subsidiaries,
are free and clear of all liens, encumbrances or restrictions (other than those
imposed by applicable federal or state securities laws) and there are no
agreements or understandings with respect to the voting or disposition of any
such shares.

               (ii)  No Voting Debt of RCFC is issued or outstanding.
 
               (iii)  As of the date of this Agreement, except for this
Agreement and as set forth in RCFC's Disclosure Letter, neither RCFC nor any of
its Subsidiaries has or is bound by any outstanding options, warrants, calls,
rights, convertible securities, commitments or agreements of any character
obligating RCFC or any of its Subsidiaries to issue, deliver or sell, or cause
to be issued, delivered or sold, any additional shares of capital stock of RCFC
or any of its Subsidiaries or obligating RCFC or any of its Subsidiaries to
grant, extend or enter into any such option, warrant, call, right, convertible
security, commitment or agreement. As of the date hereof, there are no
outstanding contractual obligations of RCFC or any of its Subsidiaries to
repurchase, redeem or otherwise acquire any shares of capital stock of RCFC or
any of its Subsidiaries.

          (c)  Authority.   Each of RCFC and RCFC Bank has the requisite
               ---------                                                
corporate power and authority to enter into this Agreement, the Option Agreement
and the Plan of Bank Merger, respectively and, subject to approval of this
Agreement, by the requisite vote of RCFC's stockholders and receipt of all
required regulatory or governmental approvals, as contemplated by Section 5.1(b)
of this Agreement, to consummate the transactions contemplated hereby.  The
execution and delivery of this Agreement and the Option Agreement, and, subject
to the approval of this Agreement by RCFC's stockholders, the consummation of
the transactions contemplated 

                                       26
<PAGE>
 
hereby, have been duly authorized by all necessary corporate actions on the part
of RCFC and RCFC Bank. This Agreement and the Option Agreement have been duly
executed and delivered by RCFC and constitutes a valid and binding obligations
of RCFC, enforceable in accordance with its terms subject to applicable
bankruptcy, insolvency and similar laws affecting creditors' rights and remedies
generally and subject, as to enforceability, to general principles of equity,
whether applied in a court of law or a court of equity.

          (d)  Stockholder Approval; Fairness Opinion.  The affirmative vote of
               --------------------------------------                           
a majority of the outstanding shares of RCFC Common Stock entitled to vote on
this Agreement is the only vote of the stockholders of RCFC required for
approval of the Agreement and the consummation of the Merger and the related
transactions contemplated hereby.  RCFC has received the opinion of Tucker
Anthony Incorporated, to the effect that, as of the date hereof, the Exchange
Ratio is fair, from a financial point of view, to RCFC's stockholders.

          (e)  No Violations.  The execution, delivery and performance of this
               -------------                                                  
Agreement by RCFC does not, and the consummation of the transactions
contemplated hereby will not, constitute (i) assuming receipt of all Requisite
Regulatory Approvals and requisite stockholder approvals, a breach or violation
of, or a default under, any law, rule or regulation or any judgment, decree,
order, governmental permit or license, or agreement, indenture or instrument of
RCFC or any of its Subsidiaries, or to which RCFC or any of its Subsidiaries (or
any of their respective properties) is subject, (ii) a breach or violation of,
or a default under, the certificate of incorporation or bylaws of RCFC or the
similar organizational documents of any of its Subsidiaries or (iii) a breach or
violation of, or a default under (or an event which, with due notice or lapse of
time or both, would constitute a default under), or result in the termination
of, accelerate the performance required by, or result in the creation of any
lien, pledge, security interest, charge or other encumbrance upon any of the
properties or assets of RCFC or any of its Subsidiaries, under, any of the
terms, conditions or provisions of any note, bond, indenture, deed of trust,
loan agreement or other agreement, instrument or obligation to which RCFC or any
of its Subsidiaries is a party, or to which any of their respective properties
or assets may be subject; and the consummation of the transactions (including
the Bank Merger) contemplated hereby (exclusive of the effect of any changes
effected pursuant to Section 1.7) will not require any approval, consent or
waiver under any such law, rule, regulation, judgment, decree, order,
governmental permit or license or the approval, consent or waiver of any other
party to any such agreement, indenture or instrument, other than (x) the
approval of the holders of a majority of the outstanding shares of RCFC Common
Stock, (y) the approval of the Banking Board of the State of New York ("Banking
Board") under Section 143-b of the Banking Law of the Sate of New York ("Banking
Law"), the approval of the Superintendent of Banks of the State of New York (the
"Superintendent") under Section 601 of the Banking Law and any other requirement
of the Banking Board or the Superintendent, the approval of the OTS, under HOLA,
the approval of the NJBD and the approval of the appropriate regulatory
authority under Section 18(c) of the FDIC (collectively, the "Requisite
Regulatory Approvals") and (z) such approvals, consents or waivers as are
required under the federal and state securities or "blue sky" laws in connection
with the transactions contemplated by this Agreement.  As of the date hereof,
the executive officers of 

                                       27
<PAGE>
 
RCFC know of no reason pertaining to RCFC why any of the approvals referred to
in this Section 2.4(e) should not be obtained without the imposition of any
material condition or restriction described in the proviso to Section 5.1(b).

          (f)  Reports.  (i)  As of their respective dates, none of the reports
               -------                                                         
or other statements filed by RCFC or RCFC Bank on or subsequent to December 31,
1997, with the FDIC or the SEC (collectively, "RCFC's Reports"), contained, or
will contain, any untrue statement of a material fact or omitted or will omit to
state a material fact required to be stated therein or necessary to make the
statements made therein, in light of the circumstances under which they were
made, not misleading.  Each of the financial statements of RCFC included in
RCFC's Reports complied as to form, as of their respective dates of filing with
the SEC, in all material respects with applicable accounting requirements and
with the published rules and regulations of the SEC with respect thereto and
have been prepared in accordance with GAAP (except as may be indicated in the
notes thereto or, in the case of unaudited financial statements, as permitted by
Form 10-Q of the SEC).  Each of the consolidated statements of condition
contained or incorporated by reference in RCFC's Reports (including in each case
any related notes and schedules) and each of the statements of operations,
consolidated statements of cash flows and consolidated statements of changes in
stockholders' equity, contained or incorporated by reference in RCFC's Reports
(including in each case any related notes and schedules) fairly presented, or
will fairly present, as the case may be, (A) the financial position of the
entity or entities to which it relates as of its date,  and (B) the results of
operations, stockholders' equity and cash flows, as the case may be, of the
entity or entities to which it relates for the periods set forth therein
(subject, in the case of unaudited interim statements, to normal year-end audit
adjustments that are not material in amount or effect), in each case in
accordance with GAAP, except as may be noted therein.  RCFC has made available
to Bayonne a true and complete copy of each of RCFC's Reports filed with the SEC
since December 31, 1997.

               (ii)  RCFC and each of its Subsidiaries have each timely filed
all material reports, registrations and statements, together with any amendments
required to be made with respect thereto, that they were required to file since
December 31, 1993 with (A) the FDIC, (B) the SEC, (C) the NASD, (D) the NYBD and
(E) any other SRO, and, to RCFC's knowledge, have paid all fees and assessments
due and payable in connection therewith.

          (g)  Absence of Certain Changes or Events.   Except as disclosed in
               ------------------------------------                          
RCFC's Reports filed on or prior to the date of this Agreement, since December
31, 1997, (i) RCFC and its Subsidiaries have not incurred any liability, except
in the ordinary course of their business consistent with past practice, (ii)
RCFC and its Subsidiaries have conducted their respective businesses only in the
ordinary and usual course of such businesses and (iii) there has not been any
Material Adverse Effect with respect to RCFC.

          (h)  Absence of Claims.  Except as set forth in RCFC's Disclosure
               -----------------                                           
Letter, no litigation, proceeding, controversy, claim or action before any court
or governmental agency is 

                                       28
<PAGE>
 
pending against RCFC or any of its Subsidiaries, and, to the best of RCFC's
knowledge, no such litigation, proceeding, controversy, claim or action has been
threatened.

          (i)  Absence of Regulatory Actions.  Neither RCFC nor any of its
               -----------------------------                              
Subsidiaries is a party to any cease and desist order, written agreement or
memorandum of understanding with, or  any commitment letter or similar written
undertaking to, or is subject to any action, proceeding, order or directive by,
or is a recipient of any extraordinary supervisory letter from any Government
Regulator, or has adopted any board resolutions at the request of any Government
Regulator, nor has it been advised by any Governmental Regulator that it is
contemplating issuing or requesting (or is considering the appropriateness of
issuing or requesting) any such action, proceeding, order, directive, written
agreement, memorandum of understanding, extraordinary supervisory letter,
commitment letter, board resolutions  or similar written undertaking.

          (j)  Taxes.  All federal, state, local and foreign tax returns 
               -----        
required to be filed by or on behalf of RCFC or any of its Subsidiaries have
been timely filed or requests for extensions have been timely filed and any such
extension shall have been granted and not have expired, and all such filed
returns are complete and accurate in all material respects. All taxes shown on
such returns, all taxes required to be shown on returns for which extensions
have been granted and all other taxes required to be paid by RCFC or any of its
Subsidiaries have been paid in full or adequate provision has been made for any
such taxes on RCFC's balance sheet (in accordance with GAAP). For purposes of
this Section 2.4(j), the term "taxes" shall include all income, franchise, gross
receipts, real and personal property, real property transfer and gains, wage and
employment taxes. As of the date of this Agreement, there is no audit
examination, deficiency assessment, tax investigation or refund litigation with
respect to any taxes of RCFC or any of its Subsidiaries, and no claim has been
made by any authority in a jurisdiction where RCFC or any of its Subsidiaries do
not file tax returns that RCFC or any such Subsidiary is subject to taxation in
that jurisdiction. All taxes, interest, additions and penalties due with respect
to completed and settled examinations or concluded litigation relating to RCFC
or any of its Subsidiaries have been paid in full or adequate provision has been
made for any such taxes on RCFC's balance sheet (in accordance with GAAP).
Except as set forth in RCFC's Disclosure Letter, RCFC and its Subsidiaries have
not executed an extension or waiver of any statute of limitations on the
assessment or collection of any material tax due that is currently in effect.
RCFC and each of its Subsidiaries has withheld and paid all taxes required to
have been withheld and paid in connection with amounts paid or owing to any
employee, independent contractor, creditor, stockholder or other third party,
and RCFC and each of its Subsidiaries has timely complied with all applicable
information reporting requirements under Part III, Subchapter A of Chapter 61 of
the Code and similar applicable state and local information reporting
requirements. Neither RCFC nor any of its Subsidiaries (i) has made an election
under Section 341(f) of the Code, (ii) has issued or assumed any obligation
under Section 279 of the Code, any high yield discount obligation as described
in Section 163(i) of the Code or any registration-required obligation within the
meaning of Section 163(f)(2) of the Code that is not in registered form or 

                                       29
<PAGE>
 
(iii) is or has been a United States real property holding corporation within
the meaning of Section 897(c)(2) of the Code.

          (k)  Agreements.  (i)  Except for arrangements made in the ordinary
               ----------                                                       
course of business, and except as set forth in RCFC's Disclosure Letter, RCFC
and its Subsidiaries are not bound by any material contract (as defined in Item
601(b)(10) of Regulation S-K) to be performed after the date hereof that has not
been filed with or incorporated by reference in RCFC's Reports.  Except as
disclosed in RCFC's Reports filed prior to the date of this Agreement, neither
RCFC nor any of its Subsidiaries is a party to an oral or written (A) consulting
agreement (other than data processing, software programming and licensing
contracts entered into in the ordinary course of business) not terminable on 60
days' or less notice, (B) agreement with any executive officer or other key
employee of RCFC or any of its Subsidiaries the benefits of which are
contingent, or the terms of which are materially altered, upon the occurrence of
a transaction involving RCFC or any of its Subsidiaries of the nature
contemplated by this Agreement, (C) agreement with respect to any employee or
director of RCFC or any of its Subsidiaries providing any term of employment or
compensation guarantee extending for a period longer than 60 days or for the
payment of in excess of $100,000 per annum, (D) agreement or plan, including any
stock option plan, phantom stock or stock appreciation rights plan, restricted
stock plan or stock purchase plan, any of the benefits of which will be
increased, or the vesting or payment of the benefits of which will be
accelerated, by the occurrence of a transaction involving RCFC or any of its
Subsidiaries of the nature contemplated by this Agreement or the value of any of
the benefits of which will be calculated on the basis of a transaction of the
nature contemplated by this Agreement or (E) agreement containing covenants that
limit the ability of RCFC or any of its Subsidiaries to compete in any line of
business or with any person, or that involve any restriction on the geographic
area in which, or method by which, RCFC (including any successor thereof) or any
of its Subsidiaries may carry on its business (other than as may be required by
law or any regulatory agency).

               (ii)  Neither RCFC nor any of its Subsidiaries is in default
under or in violation of any provision of any note, bond, indenture, mortgage,
deed of trust, loan agreement, lease or other agreement to which it is a party
or by which it is bound or to which any of its respective properties or assets
is subject.

               (iii)  RCFC and each of its Subsidiaries owns or possesses
valid and binding licenses and other rights to use without payment all patents,
copyrights, trade secrets, trade names, servicemarks and trademarks used in its
businesses, and neither RCFC nor any of its Subsidiaries has received any notice
of conflict with respect thereto that asserts the right of others.  Each of RCFC
and its Subsidiaries has performed all the obligations required to be performed
by it and are not in default under any contract, agreement, arrangement or
commitment relating to any of the foregoing.

          (l)  RCFC Common Stock.  The shares of RCFC Common Stock to be issued
               -----------------                                               
pursuant to this Agreement, when issued in accordance with the terms of this
Agreement, will be 

                                       30
<PAGE>
 
duly authorized, validly issued, fully paid and non-assessable and subject to no
preemptive rights.

          (m)  Labor Matters.  Neither RCFC nor any of its Subsidiaries is or 
               -------------        
has ever been a party to, or is or has ever been bound by, any collective
bargaining agreement, contract or other agreement or understanding with a labor
union or labor organization with respect to its employees, nor is RCFC or any of
its Subsidiaries the subject of any proceeding asserting that it has committed
an unfair labor practice or seeking to compel RCFC or any of its Subsidiaries to
bargain with any labor organization as to wages and conditions of employment,
nor is there any strike, other labor dispute or organizational effort involving
RCFC or any of its Subsidiaries pending or, to RCFC's knowledge, threatened.
RCFC and its Subsidiaries are in compliance with applicable laws regarding
employment of employees and retention of independent contractors and are in
compliance with applicable employment tax laws.

          (n)  Employee Benefit Plans.  RCFC's Disclosure Letter contains a
               ----------------------                                      
complete and accurate list of all pension, retirement, stock option, stock
purchase, stock ownership, savings, stock appreciation right, profit sharing,
deferred compensation, consulting, bonus, group insurance, severance and other
benefit plans, contracts, agreements and arrangements, including, but not
limited to, "employee benefit plans," as defined in Section 3(3) of ERISA,
incentive and welfare policies, contracts, plans and arrangements and all trust
agreements related thereto with respect to any present or former directors,
officers or other employees of RCFC or any of its Subsidiaries (hereinafter
referred to collectively as the "RCFC Employee Plans").  All of the RCFC
Employee Plans comply in all material respects with all applicable requirements
of ERISA, the Code and other applicable laws; there has occurred no "prohibited
transaction" (as defined in Section 406 of ERISA or Section 4975 of the Code)
which is likely to result in the imposition of any penalties or taxes under
Section 502(i) of ERISA or Section 4975 of the Code upon RCFC or any of its
Subsidiaries.  No liability to the PBGC has been or is expected by RCFC or any
of its Subsidiaries to be incurred with respect to any RCFC Employee Plan which
is subject to Title IV of ERISA ("RCFC Pension Plan"), or with respect to any
"single-employer plan" (as defined in Section 4001(a) of ERISA) currently or
formerly maintained by RCFC or any entity which is considered one employer with
RCFC under Section 4001(b)(1) of ERISA or Section 414 of the Code (an "ERISA
Affiliate").  No RCFC Pension Plan had an "accumulated funding deficiency" (as
defined in Section 302 of ERISA), whether or not waived, as of the last day of
the end of the most recent plan year ending prior to the date hereof; the fair
market value of the assets of each RCFC Pension Plan exceeds the present value
of the "benefit liabilities" (as defined in Section 4001(a)(16) of ERISA) under
such RCFC Pension Plan as of the end of the most recent plan year with respect
to the respective RCFC Pension Plan ending prior to the date hereof, calculated
on the basis of the actuarial assumptions used in the most recent actuarial
valuation for such RCFC Pension Plan as of the date hereof; and no notice of a
"reportable event" (as defined in Section 4043 of ERISA) for which the 30-day
reporting requirement has not been waived has been required to be filed for any
RCFC Pension Plan within the 12-month period ending on the date hereof. Neither
RCFC nor any of its Subsidiaries has provided, or is required to provide,
security to any RCFC Pension Plan or to any single-employer plan of an 

                                       31
<PAGE>
 
ERISA Affiliate pursuant to Section 401(a)(29) of the Code. Neither RCFC, its
Subsidiaries, nor any ERISA Affiliate has contributed to any "multiemployer
plan," as defined in Section 3(37) of ERISA, on or after September 26, 1980.
Each RCFC Employee Plan that is an "employee pension benefit plan" (as defined
in Section 3(2) of ERISA) and which is intended to be qualified under Section
401(a) of the Code (an "RCFC Qualified Plan") has received a favorable
determination letter from the IRS, and RCFC and its Subsidiaries are not aware
of any circumstances likely to result in revocation of any such favorable
determination letter. Each RCFC Qualified Plan that is an "employee stock
ownership plan" (as defined in Section 4975(e)(7) of the Code) has satisfied all
of the applicable requirements of Sections 409 and 4975(e)(7) of the Code and
the regulations thereunder in all respects and any assets of any such RCFC
Qualified Plan that are not allocated to participants' individual accounts are
pledged as security for, and may be applied to satisfy, any securities
acquisition indebtedness. There is no pending or, to RCFC's knowledge,
threatened litigation, administrative action or proceeding relating to any RCFC
Employee Plan. There has been no announcement or commitment by RCFC or any of
its Subsidiaries to create an additional RCFC Employee Plan, or to amend any
RCFC Employee Plan, except for amendments required by applicable law which do
not materially increase the cost of such RCFC Employee Plan; and, except as
specifically identified in RCFC's Disclosure Letter, RCFC and its Subsidiaries
do not have any obligations for post-retirement or post-employment benefits
under any RCFC Employee Plan that cannot be amended or terminated upon 60 days'
notice or less without incurring any liability thereunder, except for coverage
required by Part 6 of Title I of ERISA or Section 4980B of the Code, or similar
state laws, the cost of which is borne by the insured individuals. With respect
to RCFC or any of its Subsidiaries, for the Employee Plans listed in RCFC's
Disclosure Letter, the execution and delivery of this Agreement and the
consummation of the transactions contemplated hereby will not result in any
payment or series of payments by RCFC or any of its Subsidiaries to any person
which is an "excess parachute payment" (as defined in Section 280G of the Code),
increase or secure (by way of a trust or other vehicle) any benefits payable
under any RCFC Employee Plan or accelerate the time of payment or vesting of any
such benefit. With respect to each RCFC Employee Plan, RCFC has supplied to
Bayonne a true and correct copy of (A) the annual report on the applicable form
of the Form 5500 series filed with the IRS for the most recent three plan years,
if required to be filed, (B) such RCFC Employee Plan, including amendments
thereto, (C) each trust agreement, insurance contract or other funding
arrangement relating to such RCFC Employee Plan, including amendments thereto,
(D) the most recent summary plan description and summary of material
modifications thereto for such RCFC Employee Plan, if the RCFC Employee Plan is
subject to Title I of ERISA, (E) the most recent actuarial report or valuation
if such RCFC Employee Plan is an RCFC Pension Plan and any subsequent changes to
the actuarial assumptions contained therein and (F) the most recent
determination letter issued by the IRS if such RCFC Employee Plan is a Qualified
Plan.

          (o)  Title to Assets.  RCFC and each of its Subsidiaries has good and
               ---------------                                                 
marketable title to its properties and assets (including any intellectual
property asset such as any trademark, service mark, tradename or copyright) and
property acquired in a judicial foreclosure proceeding or by way of a deed in
lieu of foreclosure or similar transfer, other than property as to 

                                       32
<PAGE>
 
which it is lessee, in which case the related lease is valid and in full force
and effect. Each lease pursuant to which RCFC or any of its Subsidiaries is
lessor is valid and in full force and effect and no lessee under any such lease
is in default or in violation of any provisions of any such lease. All material
tangible properties of RCFC and each of its Subsidiaries are in a good state of
maintenance and repair, conform with all applicable ordinances, regulations and
zoning laws and are considered by RCFC to be adequate for the current business
of RCFC and its Subsidiaries.

          (p)  Compliance with Laws.  RCFC and each of its Subsidiaries has all
               --------------------                                            
permits, licenses, certificates of authority, orders and approvals of, and has
made all filings, applications and registrations with, all federal, state, local
and foreign governmental or regulatory bodies that are required in order to
permit it to carry on its business as it is presently conducted; all such
permits, licenses, certificates of authority, orders and approvals are in full
force and effect, and, to the best knowledge of RCFC, no suspension or
cancellation of any of them is threatened.  Since the date of its incorporation,
the corporate affairs of RCFC have not been conducted in violation of any law,
ordinance, regulation, order, writ, rule, decree or approval of any Governmental
Entity.  The businesses of RCFC and its Subsidiaries are not being conducted in
violation of any law, ordinance, regulation, order, writ, rule, decree or
condition to approval of any Governmental Entity.  The businesses of RCFC and
its Subsidiaries are not being conducted in violation of any law, ordinance,
regulation, order, writ, rule, decree or condition to approve of any Government
Entity.

          (q)  Fees.  Other than the financial advisory services performed for
               ----                                                           
RCFC by Tucker Anthony Incorporated pursuant to an agreement with RCFC dated
July 19, 1998, a true and complete copy of which has been previously delivered
to Bayonne, neither RCFC nor any of its Subsidiaries, nor any of their
respective officers, directors, employees or agents, has employed any broker or
finder or incurred any liability for any financial advisory fees, brokerage
fees, commissions or finder's fees, and no broker or finder has acted directly
or indirectly for RCFC or any of its Subsidiaries in connection with this
Agreement or the transactions contemplated hereby.

          (r)  Environmental Matters.  With respect to RCFC and each of its
               ---------------------                                       
Subsidiaries:

               (i)  Each of RCFC and its Subsidiaries, the Participation
Facilities and, to RCFC's knowledge, the Loan Properties are, and have been, in
substantial compliance with, and are not liable under, all Environmental Laws;

               (ii)  There is no suit, claim, action, demand, executive or
administrative order, directive, investigation or proceeding pending or, to
RCFC's knowledge, threatened, before any court, governmental agency or board or
other forum against it or any of its Subsidiaries or any Participation Facility
(x) for alleged noncompliance (including by any predecessor) with, or liability
under, any Environmental Law or (y) relating to the presence of or release into
the environment of any Hazardous Material, whether or not occurring at or on a
site owned, leased or operated by it or any of its Subsidiaries or any
Participation Facility;

                                       33
<PAGE>
 
               (iii)  To RCFC's knowledge, there is no suit, claim, action,
demand, executive or administrative order, directive, investigation or
proceeding pending or threatened before any court, governmental agency or board
or other forum relating to or against any Loan Property (or RCFC or any of its
Subsidiaries in respect of such Loan Property) (x) relating to alleged
noncompliance (including by any predecessor) with, or liability under, any
Environmental Law or (y) relating to the presence of or release into the
environment of any Hazardous Material, whether or not occurring at or on a site
owned, leased or operated by a Loan Property;

               (iv)  To RCFC's knowledge, the properties currently owned or
operated by RCFC or any of its Subsidiaries (including, without limitation,
soil, groundwater or surface water on, under or adjacent to the properties, and
buildings thereon) are not contaminated with and do not otherwise contain any
Hazardous Material other than as permitted under applicable Environmental Law;

               (v)  Neither RCFC nor any of its Subsidiaries has received any
notice, demand letter, executive or administrative order, directive or request
for information from any federal, state, local or foreign governmental entity or
any third party indicating that it may be in violation of, or liable under, any
Environmental Law;

               (vi)  To RCFC's knowledge, there are no underground storage tanks
on, in or under any properties owned or operated by RCFC or any of its
Subsidiaries or any Participation Facility and no underground storage tanks have
been closed or removed from any properties owned or operated by RCFC or any of
its Subsidiaries or any Participation Facility; and

               (vii)  To RCFC's knowledge, during the period of (l) RCFC's or
any of its Subsidiaries' ownership or operation of any of their respective
current properties or (m) RCFC's or any of its Subsidiaries' participation in
the management of any Participation Facility, there has been no contamination by
or release of Hazardous Materials in, on, under or affecting such properties.
To RCFC's knowledge, prior to the period of (x) RCFC's or any of its
Subsidiaries' ownership or operation of any of their respective current
properties or (y) RCFC's or any of its Subsidiaries' participation in the
management of any Participation Facility, there was no contamination by or
release of Hazardous Material in, on, under or affecting  such property,
Participation Facility or Loan Property.

          (s)  Loan Portfolio; Allowance; Asset Quality.  (i)  With respect to
               ----------------------------------------                        
each Loan owned by RCFC or its Subsidiaries in whole or in part, to RCFC's best
knowledge:

               (A)  the note and the related security documents are each legal,
valid and binding obligations of the maker or obligor thereof, enforceable
against such maker or obligor in accordance with their terms;

                                       34
<PAGE>
 
               (B)  neither RCFC nor any of its Subsidiaries nor any prior
holder of a Loan has modified the note or any of the related security documents
in any material respect or satisfied, canceled or subordinated the note or any
of the related security documents except as otherwise disclosed by documents in
the applicable Loan file;

               (C)  RCFC or a Subsidiary is the sole holder of legal and
beneficial title to each Loan (or RCFC Bank's applicable participation interest,
as applicable); except as otherwise referenced on the books and records of RCFC;

               (D)  the note and the related security documents, copies of which
are included in the Loan files, are true and correct copies of the documents
they purport to be and have not been suspended, amended, modified, canceled or
otherwise changed except as otherwise disclosed by documents in the applicable
Loan file;

               (E)  there is no pending or threatened condemnation proceeding or
similar proceeding affecting the property that serves as security for a Loan;
except as otherwise referenced on the books and records of RCFC;

               (F)  there is no litigation or proceeding pending or threatened
relating to the property that serves as security for a Loan that would have a
Material Adverse Effect upon the related Loan; and

               (G)  with respect to a Loan held in the form of a participation,
the participation documentation is legal, valid, binding and enforceable.

               (ii)  The allowance for possible losses reflected in RCFC Bank's
audited statement of condition at June 30, 1997 was, and the allowance for
possible losses shown on the balance sheets in RCFC's Reports for periods ending
after June 30, 1997 will, in the opinion of management, be adequate, as of the
dates thereof, under generally accepted accounting principles applicable to
stock savings associations consistently applied.

               (iii)  RCFC's Disclosure Letter sets forth by category the
amounts of all loans, leases, advances, credit enhancements, other extensions of
credit, commitments and interest-bearing assets of RCFC and its Subsidiaries
that have been classified (whether regulatory or internal) as "Other Loans
Specially Mentioned," "Special Mention," "Substandard," "Doubtful," "Loss,"
"Classified," "Criticized," "Credit Risk Assets," "Concerned Loans" (in the
latter two cases, to the extent available) or words of similar import, and RCFC
and its Subsidiaries shall promptly after the end of any month inform Bayonne of
any such classification arrived at any time after the date hereof. The OREO or
words of similar import included in any non-performing assets of RCFC or any of
its Subsidiaries is carried net of reserves at the lower of cost or fair value,
less estimated selling costs, based on current independent appraisals or
evaluations or current management appraisals or evaluations; provided, however,
that "current" shall mean within the past 12 months.

                                       35
<PAGE>
 
          (t)  Accounting Matters.  Neither RCFC nor any of its Subsidiaries or,
               ------------------                                               
to the best of RCFC's knowledge, any of its other affiliates has, through the
date hereof, taken or agreed to take any action that would prevent RCFC from
accounting for the business combination contemplated herein as a pooling-of-
interests, and RCFC has no knowledge of any fact or circumstance relating to it
that would prevent such accounting treatment.

          (u)  Investment Securities; Borrowing.  (i)  Except for investments in
               --------------------------------                                 
FHLB Stock and pledges to secure FHLB borrowings and reverse repurchase
agreements entered into in arms-length transactions pursuant to normal
commercial terms and conditions and entered into in the ordinary course of
business and restrictions that exist for securities to be classified as "held to
maturity," none of the investments reflected in the consolidated balance sheet
of RCFC included in RCFC's Report on Form 10-K for the year ended December 31,
1997, and none of the investment securities held by it or any of its
Subsidiaries since December 31, 1997 is subject to any restriction (contractual
or statutory) that would materially impair the ability of the entity holding
such investment freely to dispose of such investment at any time.

               (ii)  Except as set forth in RCFC's Disclosure Letter, neither
RCFC nor any Subsidiary is a party to or has agreed to enter into any
Derivatives Contract or owns securities that (A) are referred to generically as
"structured notes," "high risk mortgage derivatives," "capped floating rate
notes" or "capped floating rate mortgage derivatives" or (B) are likely to have
changes in value as a result of interest or exchange rate changes that
significantly exceed normal changes in value attributable to interest or
exchange rate changes, except for those Derivatives Contracts and other
instruments legally purchased or entered into in the ordinary course of
business, consistent with safe and sound banking practices and regulatory
guidance, and listed (as of the date hereof) in RCFC's Disclosure Letter or
disclosed in RCFC's Report filed on or prior to the date hereof.

               (iii)  Set forth in RCFC's Disclosure Letter is a true and
complete list of RCFC's borrowed funds (excluding deposit accounts) as of the
date hereof.

          (v)  Registration Statement.  The information regarding RCFC to be
               ----------------------                                       
supplied by RCFC for inclusion in (i) the Registration Statement, (ii) the Proxy
Statement or (iii) any other documents to be filed with any Regulatory Authority
in connection with the transactions contemplated hereby will not, at the time
such Registration Statement becomes effective, contain any untrue statement of a
material fact or omit to state any material fact required to be stated therein
or necessary in order to make the statements therein, in light of the
circumstances under which they are made, not misleading.  All documents that
RCFC is responsible for filing in connection with the transactions contemplated
hereby will comply as to form in all material respects with the provisions of
applicable law.

          (w)  Books and Records.  The books and records of RCFC and its
               -----------------                                        
Subsidiaries on a consolidated basis have been, and are being, maintained in
accordance with applicable legal 

                                       36
<PAGE>
 
and accounting requirements and reflect in all material respects the substance
of events and transactions that should be included therein.

          (x)  Corporate Documents.  RCFC has delivered to Bayonne true and
               -------------------                                         
complete copies of its organization certificate and bylaws and of RCFC Bank's
organization certificate and bylaws.  The minute books of RCFC and RCFC Bank
constitute a complete and correct record of all actions taken by their
respective boards of directors (and each committee thereof) and their
stockholders.  The minute books of each of RCFC's Subsidiaries constitutes a
complete and correct record of all actions taken by the respective boards of
directors (and each committee thereof) and the stockholders of each such
Subsidiary.

          (y)  Beneficial Ownership of Bayonne Common Stock.  As of the date
               --------------------------------------------                 
hereof, RCFC beneficially owns 442,500 shares of Bayonne Common Stock and, other
than as contemplated by the Option Agreement, does not have any option, warrant
or right of any kind to acquire the beneficial ownership of any shares of
Bayonne Common Stock.

          (z)  Tax Treatment of the Merger.  As of the date hereof, RCFC has no
               ---------------------------                                     
knowledge of any fact or circumstance relating to it that would prevent the
transactions contemplated by this Agreement from qualifying as a tax-free
reorganization under the Code.

          (aa) Year 2000 Matters.  RCFC has completed a review of its computer
               -----------------                                              
systems to identify systems that could be affected by the "Year 2000" issue and
reasonably believes it has identified all Year 2000 problems.  RCFC's management
has developed and commenced implementation of a plan which is designed to
complete any required initial changes to its computer systems and to complete
testing of those changes by December 31, 1998. Between the date of this
Agreement and the Effective Time, RCFC shall use commercially practicable
efforts to implement and/or continue to undertake such plan.  Year 2000 issues
have not had, and are not reasonably expected to have, a Material Adverse Effect
on RCFC and its Subsidiaries, taken as a whole.

          (bb) Community Reinvestment Act ("CRA") Compliance.  RCFC Bank is in
               ---------------------------------------------                  
material compliance with the applicable provisions of the CRA and the
regulations promulgated thereunder, and RCFC Bank currently has a CRA rating of
satisfactory or better.  To RCFC's knowledge, there is no fact or circumstance
or set of facts or circumstances that would cause RCFC Bank to fail to comply
with such provisions or cause the CRA rating of RCFC Bank to fall below
satisfactory.


                                  ARTICLE III
                           CONDUCT PENDING THE MERGER
                           --------------------------

          Section 3.1.  Conduct of Bayonne's Business Prior to the Effective
                        ----------------------------------------------------
Time.  Except as expressly provided in this Agreement, during the period from 
- ----                                                                            
the date of this Agreement to the Effective Time, Bayonne shall, and shall cause
its Subsidiaries to, use 

                                       37
<PAGE>
 
commercially reasonable efforts to (i) conduct its business in the regular,
ordinary and usual course consistent with past practice; (ii) maintain and
preserve intact its business organization, properties, leases, employees and
advantageous business relationships and retain the services of its officers and
key employees, (iii) take no action which would adversely affect or delay the
ability of Bayonne or RCFC to perform their respective covenants and agreements
on a timely basis under this Agreement, (iv) take no action which would
adversely affect or delay the ability of Bayonne, First Savings, RCFC or RCFC
Bank to obtain any necessary approvals, consents or waivers of any governmental
authority required for the transactions contemplated hereby or which would
reasonably be expected to result in any such approvals, consents or waivers
containing any material condition or restriction, and (v) take no action that
results in or is reasonably likely to have a Material Adverse Effect on Bayonne
or First Savings.

          Section 3.2.  Forbearance by Bayonne.  Without limiting the covenants
                        ----------------------                                 
set forth in Section 3.1 hereof, except as otherwise provided in this Agreement
and except to the extent required by law or regulation or any Government
Regulators, during the period from the date of this Agreement to the Effective
Time, Bayonne shall not, and shall not permit any of its Subsidiaries to,
without the prior consent of RCFC, which consent shall not be unreasonably
withheld:

          (a)  unless required by applicable law or regulation or regulatory
directive, change any provisions of the certificate of incorporation or bylaws
of Bayonne or the similar governing documents of its Subsidiaries;

          (b)  issue any shares of capital stock or change the terms of any
outstanding stock options or warrants or issue, grant or sell any option,
warrant, call, commitment, stock appreciation right, right to purchase or
agreement of any character relating to the authorized or issued capital stock of
Bayonne except pursuant to the exercise of stock options or warrants outstanding
as of the date of this Agreement;

          (c)  other than regular quarterly dividends, make, declare or pay any
cash or stock dividend or make any other distribution on, or directly or
indirectly redeem, purchase or otherwise acquire, any shares of its capital
stock or any securities or obligations convertible into or exchangeable for any
shares of its capital stock.  As promptly as practicable following the date of
this Agreement, the Board of Directors of Bayonne shall cause its regular
quarterly dividend record dates and payment dates to be the same as RCFC's
regular quarterly dividend record dates and payments dates for RCFC Common
Stock, and Bayonne shall not thereafter change its regular dividend payment
dates and record dates.  Nothing contained in this Section 3.2(c) or in any
other Section of this Agreement shall be construed to permit holders of shares
of Bayonne Common Stock to receive two dividends from either Bayonne or from
Bayonne and RCFC in any one quarter.  Subject to applicable regulatory
restrictions, if any, First Savings may pay a cash dividend that is, in the
aggregate, sufficient to fund any dividend by Bayonne permitted hereunder;

                                       38
<PAGE>
 
          (d)  other than in the ordinary course of business consistent with
past practice, (i) sell, transfer, mortgage, encumber or otherwise dispose of
any of its material properties, leases or assets to any individual, corporation
or other entity other than a direct or indirect wholly owned Subsidiary of
Bayonne or (ii) cancel, release or assign any indebtedness of any such
individual, corporation or other entity;

          (e)  except to the extent required by law or as specifically provided
for elsewhere herein, increase in any manner the compensation or fringe benefits
of any of its employees or directors, other than general increases in
compensation for non-executive officer employees in the ordinary course of
business consistent with past practice that do not cause the annualized
compensation of any of Bayonne's non-executive officer employees following such
increase to exceed by more than 5% the total annual compensation expenses of
Bayonne with respect to such person for the twelve-month period ended March 31,
1998 and that do not cause the annual rate of base salary of any of Bayonne's
non-executive officer employees to increase by more than 5% over such person's
base salary at March 31, 1998; pay, unless approved in advance by RCFC, any
reasonable "stay in place" pay where necessary or appropriate to retain key
employees; pay any pension or retirement allowance not required by any existing
plan or agreement to any such employees or directors, or become a party to,
amend or commit itself to fund or otherwise establish any trust or account
related to any Bayonne Employee Plan (as defined in Section 2.3(m)) with or for
the benefit of any employee or director; voluntarily accelerate the vesting of
any stock options or other compensation or benefit; make any discretionary
continuation to any Employee Plan; hire any employee with an annual total
compensation payment in excess of $35,000 or enter into any employment contract;
terminate or materially increase the costs to Bayonne or any Subsidiary of any
Employee Plan;

          (f)  except as contemplated by Section 4.2, change its method of
accounting as in effect at March 31, 1998, except as required by changes in GAAP
as concurred in by Bayonne's independent auditors;

          (g)  settle any claim, action or proceeding involving any liability of
Bayonne or any of its Subsidiaries for money damages in excess of $50,000 or
impose material restrictions upon the operations of Bayonne or any of its
Subsidiaries;

          (h)  acquire or agree to acquire, by merging or consolidating with, or
by purchasing a substantial equity interest in or a substantial portion of the
assets of, or by any other manner, any business or any corporation, partnership,
association or other business organization or division thereof or otherwise
acquire or agree to acquire any assets, in each case which are material,
individually or in the aggregate, to Bayonne, except in satisfaction of debts
previously contracted;

          (i)  except pursuant to commitments existing at the date hereof which
have previously been disclosed to RCFC, make any real estate loans secured by
undeveloped land or real estate located outside the State of New Jersey (other
than real estate secured by one-to-four 

                                       39
<PAGE>
 
family homes) or make any construction loan (other than construction loans
secured by one-to-four family homes) outside the State of New Jersey;

          (j)  establish or commit to the establishment of any new branch or
other office facilities other than those for which all regulatory approvals have
been obtained except as disclosed in the Bayonne Disclosure Schedule;

          (k)  [RESERVED];

          (l)  other than in the ordinary course of business consistent with
past practice in individual amounts not to exceed $50,000 and other than
investments for Bayonne's portfolio made in accordance with Section 3.2(m), make
any investment either by purchase of stock or securities, contributions to
capital, property transfers, or purchase of any property or assets of any other
individual, corporation or other entity;

          (m)  make any investment in any debt security, including mortgage-
backed and mortgage-related securities, other than US government and US
government agency securities with final maturities not greater than five years,
mortgage-backed or mortgage related securities which would not be considered
"high risk" securities pursuant to Thrift Bulletin Number 52 issued by the OTS
or securities of the FHLB, in each case that are purchased in the ordinary
course of business consistent with past practice;

          (n)  enter into or terminate any contract or agreement, or make any
change in any of its leases or contracts, other than with respect to those
involving aggregate payments of less than, or the provision of goods or services
with a market value of less than, $20,000 per annum and other than contracts or
agreements covered by Section 3.2(g);

          (o)  make, renegotiate, renew, increase, extend or purchase any 
(i) loan, lease (credit equivalent), advance, credit enhancement or other
extension of credit, or make any commitment in respect of any of the foregoing,
except (A) in conformity with existing lending practices in amounts not to
exceed $500,000 to any individual borrower or (B) loans or advances as to which
Bayonne has a binding obligation to make such loan or advances as of the date
hereof and a description of which has been provided by Bayonne in the Bayonne
Disclosure Schedule;

          (p)  incur any additional borrowings beyond those set forth in the
Bayonne Disclosures Schedule other than short-term (six months or less) FHLB
borrowings and reverse repurchase agreements consistent with past practice, or
pledge any of its assets to secure any borrowings other than as required
pursuant to the terms of borrowings of Bayonne or any Subsidiary in effect at
the date hereof or in connection with borrowings or reverse repurchase
agreements permitted hereunder.  Deposits shall not be deemed to be borrowings
within the meaning of this paragraph;

                                       40
<PAGE>
 
          (q)  make any capital expenditures in excess of $20,000 per
expenditure from the date of this Agreement until the Effective Date other than
pursuant to binding commitments existing on the date hereof disclosed in the
Bayonne Disclosure Schedule, other than expenditures necessary to maintain
existing assets in good repair or to make payment of necessary taxes;

          (r)  organize, capitalize, lend to or otherwise invest in any
subsidiary (other than securities of the FHLB that are purchased in the ordinary
course of business consistent with past practice);

          (s)  elect to any senior executive office any person who is not a
member of the senior executive officer team of Bayonne as of the date of this
Agreement or elect to the Board of Directors of Bayonne any person who is not a
member of the Board of Directors of Bayonne;

          (t)  agree or make any commitment to take any action that is
prohibited by this Section 3.2.

          In the event that RCFC does not respond in writing to Bayonne within 
3 business days of receipt by RCFC of a written request for Bayonne to engage in
any of the actions for which RCFC's prior written consent is required pursuant
to this Section 3.2, RCFC shall be deemed to have consented to such action. Any
request by Bayonne or response thereto by RCFC shall be made in accordance with
the notice provisions of Section 8.7, shall note that it is a request pursuant
to this Section 3.2 and shall state that a failure to respond within 3 business
days shall constitute consent.

          Section 3.3.  Conduct of RCFC's Business Prior to the Effective Time.
                        ------------------------------------------------------
Except as expressly provided in this Agreement, during the period from the date
of this Agreement to the Effective Time, RCFC shall, and shall cause its
Subsidiaries to,  use commercially reasonable efforts to (i) conduct its
business in the regular, ordinary and usual course consistent with past
practice; (ii) maintain and preserve intact its business organization,
properties, leases, employees and advantageous business relationships and retain
the services of its officers and key employees; (iii) take no action which would
materially adversely affect or delay the ability of Bayonne or RCFC to perform
their respective covenants and agreements on a timely basis under this
Agreement, (iv) take no action which would adversely affect or delay the ability
of Bayonne, RCFC, First Savings or RCFC Bank to obtain any necessary approvals,
consents or waivers of any governmental authority required for the transactions
contemplated hereby or which would reasonably be expected to result in any such
approvals, consents or waivers containing any material condition or restriction,
and (v) take no action that results in or is reasonably likely to have a
Material Adverse Effect on RCFC.

                                       41
<PAGE>
 
                                   ARTICLE IV
                                   COVENANTS
                                   ---------

          Section 4.1.  Acquisition Proposals.  From and after the date hereof
                        ---------------------                                 
until the termination of this Agreement, neither Bayonne or First Savings, nor
any of their respective officers, directors, employees, representatives, agents
or affiliates (including, without limitation, any investment banker, attorney or
accountant retained by Bayonne or any of its Subsidiaries), will, directly or
indirectly, initiate, solicit or knowingly encourage (including by way of
furnishing non-public information or assistance), or facilitate knowingly, any
inquiries or the making of any proposal that constitutes, or may reasonably be
expected to lead to, any Acquisition Proposal (as defined below), or enter into
or maintain or continue discussions or negotiate with any person or entity in
furtherance of such inquiries or to obtain an Acquisition Proposal or agree to
or endorse any Acquisition Proposal, or authorize or permit any of its officers,
directors or employees or any of its Subsidiaries or any investment banker,
financial advisor, attorney, accountant or other representative retained by any
of its Subsidiaries to take any such action, and Bayonne shall notify RCFC
orally (within 1 business day) and in writing (as promptly as practicable) of
such inquiries and proposals which it or any of its subsidiaries or any such
officer, director, employee, investment banker, financial advisor, attorney,
accountant or other representative may receive relating to any of such matters
and if such inquiry or proposal is in writing, Bayonne shall deliver to RCFC a
copy of such inquiry or proposal promptly; provided, however, that nothing
contained in this Section 4.1 shall prohibit the Board of Directors of Bayonne
from (i) furnishing information to, or entering into discussions or negotiations
with any, person or entity that makes an unsolicited written, bona fide proposal
to acquire Bayonne pursuant to a merger, consolidation, share exchange, business
combination, tender or exchange offer or other similar transaction, if, and only
to the extent that, (A) the Board of Directors of Bayonne receives a written
opinion from its independent financial advisor that such proposal may be
superior to the Merger from a financial point-of-view to Bayonne's stockholders,
(B) the Board of Directors of Bayonne, after consultation with independent legal
counsel, determines in good faith that such action is necessary for the Board of
Directors of Bayonne to comply with its fiduciary duties to stockholders under
applicable law (such proposal that satisfies (A) and (B) being referred to
herein as a "Superior Proposal") and (C) prior to furnishing such information
to, or entering into discussions or negotiations with, such person or entity,
Bayonne (x) provides reasonable notice to RCFC to the effect that it is
furnishing information to, or entering into discussions or negotiations with,
another partyand (y) receives from such person or entity an executed
confidentiality agreement in reasonably customary form, (ii) complying with Rule
14e-2 promulgated under the Exchange Act with regard to a tender or exchange
offer or (iii) failing to make or withdrawing or modifying its recommendation
and entering into a Superior Proposal if there exists a Superior Proposal and
the Board of Directors of Bayonne, after consultation with independent legal
counsel, determines in good faith that such action is necessary for the Board of
Directors of Bayonne to comply with its fiduciary duties to stockholders under
applicable law.  For purposes of this Agreement, "Acquisition Proposal" shall
mean any of the following (other than the transactions contemplated hereunder)
involving Bayonne or any of its Subsidiaries:  (i) any merger, consolidation,
share exchange, business 

                                       42
<PAGE>
 
combination, or other similar transaction; (ii) any sale, lease, exchange,
mortgage, pledge, transfer or other disposition of 15% or more of the assets of
Bayonne or First Savings, taken as a whole, in a single transaction or series of
transactions; (iii) any tender offer or exchange offer for 10% or more of the
outstanding shares of capital stock of Bayonne or the filing of a registration
statement under the Securities Act in connection therewith; or (iv) any public
announcement of a proposal, plan or intention to do any of the foregoing or any
agreement to engage in any of the foregoing.

          Section 4.2.   Certain Policies of Bayonne.
                         --------------------------- 

          (a)  At the request of RCFC, Bayonne shall cause First Savings to
modify and change its loan, litigation and real estate valuation policies and
practices (including loan classifications and levels of reserves) and investment
and asset/liability management policies and practices after the date on which
all Requisite Regulatory Approvals and stockholder approvals are received, and
after receipt of written confirmation from RCFC that it is not aware of any fact
or circumstance that would prevent completion of the Merger, and prior to the
Effective Time so as to be consistent on a mutually satisfactory basis with
those of RCFC Bank; provided, however, that Bayonne shall not be required to
take such action more than 30 days prior to the Effective Date; and provided,
further, that such policies and procedures are not prohibited by GAAP or any
applicable laws and regulations.

          (b)  Bayonne's representations, warranties and covenants contained in
this Agreement shall not be deemed to be untrue or breached in any respect for
any purpose as a consequence of any modifications or changes undertaken solely
on account of this Section 4.2. RCFC agrees to hold harmless, indemnify and
defend Bayonne and its Subsidiaries, and their respective directors, officers
and employees, for any loss, claim, liability or other damage caused by or
resulting from compliance with this Section 4.2.

          Section 4.3.   Access and Information.
                         ---------------------- 

          (a)  Upon reasonable notice, Bayonne and RCFC shall (and shall cause
their respective Subsidiaries to) afford to the other and their respective
representatives (including, without limitation, directors, officers and
employees of such party and its affiliates and counsel, accountants and other
professionals retained by such party) such reasonable access during normal
business hours throughout the period prior to the Effective Time to the books,
records (including, without limitation, tax returns and work papers of
independent auditors), properties, personnel and to such other information as
either party may reasonably request; provided, however, that no investigation
pursuant to this Section 4.3 shall affect or be deemed to modify any
representation or warranty made herein.  In furtherance, and not in limitation
of the foregoing, Bayonne shall make available to RCFC all information necessary
or appropriate for the preparation and filing of all real property and real
estate transfer tax returns and reports required by reason of the Merger or the
Bank Merger.  RCFC and Bayonne will not, and will cause their respective
representatives not to, use any information obtained pursuant to this 
Section 4.3 for any purpose unrelated to the

                                       43
<PAGE>
 
consummation of the transactions contemplated by this Agreement. Subject to the
requirements of applicable law, each of RCFC and Bayonne will keep confidential,
and will cause their respective representatives to keep confidential, all
information and documents obtained pursuant to this Section 4.3 unless such
information (i) was already known to such party or an affiliate of such party,
other than pursuant to a confidentiality agreement or other confidential
relationship, (ii) becomes available to such party or an affiliate of such party
from other sources not known by such party to be bound by a confidentiality
agreement or other obligation of secrecy, (iii) is disclosed with the prior
written approval of the other party or (iv) is or becomes readily ascertainable
from published information or trade sources. In the event that this Agreement is
terminated or the transactions contemplated by this Agreement shall otherwise
fail to be consummated, each party shall promptly cause all copies of documents
or extracts thereof containing information and data as to another party hereto
(or an affiliate of any party hereto) to be returned to the party that furnished
the same.

          (b)  During the period of time beginning on the day application
materials for the Bank Merger are initially filed with the OTS, the FDIC, the
NYBD and the NJBD and continuing to the Effective Time, including weekends and
holidays, Bayonne shall cause First Savings to provide RCFC, RCFC Bank and their
authorized agents and representatives full access to First Savings's offices
after normal business hours for the purpose of installing necessary wiring and
equipment to be utilized by RCFC Bank after the Effective Time; provided, that:

               (i)  reasonable advance notice of each entry shall be given to
First Savings and First Savings approves of each entry, which approval shall not
be unreasonably withheld;

               (ii)  First Savings shall have the right to have its employees or
contractors present to inspect the work being done;

               (iii)  to the extent practicable, such work shall be done in a
manner that will not interfere with First Savings's business conducted at any
affected branch offices;

               (iv)  all such work shall be done in compliance with all
applicable laws and government regulations, and RCFC Bank shall be responsible
for the procurement, at RCFC Bank's expense, of all required governmental or
administrative permits and approvals;

               (v)  RCFC Bank shall maintain appropriate insurance satisfactory
to First Savings in connection with any work done by RCFC Bank's agents and
representatives pursuant to this Section 4.3;

               (vi)  RCFC Bank shall reimburse First Savings for any material
out-of-pocket costs or expenses incurred by First Savings in connection with
this undertaking; and

                                       44
<PAGE>
 
               (vii)  in the event this Agreement is terminated in accordance
with Article VI hereof, RCFC Bank, within a reasonable time period and at its
sole cost and expense, will restore such offices to their condition prior to the
commencement of any such installation.

          Section 4.4.   Certain Filings, Consents and Arrangements.   RCFC
                         ------------------------------------------        
shall (a) as soon as practicable and in cooperation with Bayonne (and in any
event within 45 days after the date hereof) make, or cause to be made, any
filings and applications and provide any notices required to be filed or
provided in order to obtain all approvals, consents and waivers of governmental
authorities and third parties necessary or appropriate for the consummation of
the transactions contemplated hereby; (b) cooperate with one another in promptly
(i) determining what filings and notices are required to be made or approvals,
consents or waivers are required to be obtained under any relevant federal or
state law or regulation or under any relevant agreement or other document and
(ii) making any such filings and notices, furnishing information required in
connection therewith and seeking timely to obtain any such approvals, consents
or waivers; and (c) deliver to the other copies of the publicly available
portions of all such filings, notices and applications prior to filing.

          Section 4.5.   Antitakeover Provisions.  Bayonne and its Subsidiaries
                         -----------------------                               
shall take all steps required by any relevant federal or state law or regulation
or under any relevant agreement or other document to exempt or continue to
exempt RCFC, the Agreement, the Merger, the Bank Merger and the Option Agreement
from any provisions of an antitakeover nature in Bayonne's or its Subsidiaries'
organization certificates and bylaws and the provisions of any federal or state
antitakeover laws.

          Section 4.6.   Additional Agreements.   Subject to the terms and
                         ---------------------                            
conditions herein provided, each of the parties hereto agrees to use all
reasonable efforts to take promptly, or cause to be taken promptly, all actions
and to do promptly, or cause to be done promptly, all things necessary, proper
or advisable under applicable laws and regulations to consummate and make
effective the transactions contemplated by this Agreement, including the Bank
Merger, as expeditiously as possible, including using efforts to obtain all
necessary actions or non-actions, extensions, waivers, consents and approvals
from all applicable governmental entities, effecting all necessary
registrations, applications and filings (including, without limitation, filings
under any applicable state securities laws) and obtaining any required
contractual consents and regulatory approvals.

          Section 4.7.   Publicity.   The initial press release announcing this
                         ---------                                             
Agreement shall be a joint press release and thereafter Bayonne and RCFC shall
consult with each other in issuing any press releases or otherwise making public
statements with respect to the Merger and any other transaction contemplated
hereby and in making any filings with any governmental entity or with any
national securities exchange with respect thereto.

          Section 4.8.   Stockholders Meetings.   RCFC and Bayonne shall take
                         ---------------------                               
all action necessary, in accordance with applicable law and their respective
corporate documents, to 

                                       45
<PAGE>
 
convene a meeting of their respective stockholders (each, a "Stockholder
Meeting") as promptly as practicable for the purpose of considering and voting
on approval and adoption of the transactions provided for in this Agreement.
Except to the extent legally required for the discharge by the Board of
Directors of its fiduciary duties as advised by such Board's counsel, the Board
of Directors of each of RCFC and Bayonne shall (a) recommend at its Stockholder
Meeting that the stockholders vote in favor of and approve the transactions
provided for in this Agreement and (b) use its best efforts to solicit such
approvals. RCFC and Bayonne, in consultation with each other, shall each employ
professional proxy solicitors to assist in contacting stockholders in connection
with soliciting favorable votes on the Merger. RCFC and Bayonne shall coordinate
and cooperate with respect to the timing of their respective stockholders
meetings.

          Section 4.9.   Proxy Statements; Comfort Letters.  (i) As soon as
                         ---------------------------------                 
practicable after the date hereof, RCFC shall, in cooperation with Bayonne,
prepare a Proxy Statement-Prospectus for the purpose of taking stockholder
action on the Merger and this Agreement and subject to the provisions of Section
4.4, file the Proxy Statement-Prospectus with the SEC, respond to comments of
the staff of the SEC and, promptly after the Registration Statement is declared
effective by the SEC, mail the Proxy Statement-Prospectus to the respective
holders of record (as of the applicable record date) of shares of voting stock
of each of Bayonne and RCFC.  RCFC and Bayonne each represents and covenants to
the other that the Proxy Statement-Prospectus, and any amendment or supplement
thereto, with respect to the information pertaining to it or its Subsidiaries at
the date of mailing to its stockholders and the date of its Stockholder Meeting
will be in compliance with the Exchange Act and all relevant rules and
regulations of the SEC.

               (ii)  RCFC shall use its reasonable best efforts to cause Ernst &
Young LLP, its independent public accounting firm, to deliver to Bayonne, and
Bayonne shall use its reasonable best efforts to cause KPMG Peat Marwick LLP,
its independent public accounting firm, to deliver to RCFC and to its officers
and directors who sign the Registration Statement for this transaction, a
"comfort letter" or "agreed upon procedures" letter, in the form customarily
issued by such accountants at such time in transactions of this type, dated 
(a) the date of the mailing of the Proxy Statement-Prospectus for the
Stockholders Meeting of Bayonne and the date of mailing of the Proxy Statement
for the Stockholders meeting of RCFC, respectively, and (b) a date not earlier
than fourteen days preceding the date of the Closing (as defined in 
Section 7.1).

          Section 4.10.  Registration of RCFC Common Stock.
                         --------------------------------- 

          (a)  RCFC shall, as promptly as practicable following the preparation
thereof, file the Registration Statement in which the Proxy Statement-Prospectus
will be included (including any pre-effective or post-effective amendments or
supplements thereto) with the SEC under the Securities Act in connection with
the transactions contemplated by this Agreement, and RCFC and Bayonne shall use
all reasonable efforts to have the Registration Statement declared effective
under the Securities Act as promptly as practicable after such filing.  RCFC
will advise 

                                       46
<PAGE>
 
Bayonne promptly after RCFC receives notice of the time when the Registration
Statement has become effective or any supplement or amendment has been filed, of
the issuance of any stop order or the suspension of the qualification of the
shares of capital stock issuable pursuant to the Registration Statement, or the
initiation or threat of any proceeding for any such purpose, or of any request
by the SEC for the amendment or supplement of the Registration Statement or for
additional information. RCFC will provide Bayonne with as many copies of such
Registration Statement and all amendments thereto promptly upon the filing
thereof as Bayonne may reasonably request.

          (b)  RCFC shall use its best efforts to obtain, prior to the effective
date of the Registration Statement, all necessary state securities laws or "blue
sky" permits and approvals required to carry out the transactions contemplated
by this Agreement.

          (c)  RCFC shall use its best efforts to list, prior to the Effective
Time, on the Nasdaq National Market, or on such other exchange as RCFC Common
Stock shall then be trading, subject only to official notice of issuance, the
shares of RCFC Common Stock to be issued by RCFC in exchange for the shares of
Bayonne Common Stock.

          Section 4.11.  Affiliate Letters.   Promptly, but in any event within
                         -----------------                                     
7 days after the execution and delivery of this Agreement, Bayonne shall deliver
to RCFC a letter identifying all persons who, to the knowledge of Bayonne, may
be deemed to be "affiliates" of Bayonne under Rule 145 of the Securities Act and
the pooling-of-interests accounting rules, including, without limitation, all
directors and executive officers of Bayonne.  Within 21 days after delivery of
such letter, Bayonne shall use its best efforts to deliver executed letter
agreements, each substantially in the form attached hereto as Exhibit A,
executed by each such person so identified as an affiliate of Bayonne agreeing
(i) to comply with Rule 145, and (ii) to refrain from transferring shares as
required by the pooling-of-interests accounting rules.  Within 2 weeks after the
date hereof, RCFC shall cause its directors and executive officers to enter into
letter agreements with RCFC concerning the pooling-of-interests accounting rules
in the Form attached as Exhibit C.

          Section 4.12.  Notification of Certain Matters.   Each party shall
                         -------------------------------                    
give prompt notice to the others of: (a) any event or notice of, or other
communication relating to, a default or event that, with notice or lapse of time
or both, would become a default, received by it or any of its Subsidiaries
subsequent to the date of this Agreement and prior to the Effective Time, under
any contract material to the financial condition, properties, businesses or
results of operations of each party and its Subsidiaries taken as a whole to
which each party or any Subsidiary is a party or is subject; and (b) any event,
condition, change or occurrence which individually or in the aggregate has, or
which, so far as reasonably can be foreseen at the time of its occurrence, is
reasonably likely to result in a Material Adverse Event.  Each of Bayonne and
RCFC shall give prompt notice to the other party of any notice or other
communication from any third party alleging that the consent of such third party
is or may be required in connection with any of the transactions contemplated by
this Agreement.

                                       47
<PAGE>
 
          Section 4.13.  Employees, Directors and Officers.
                         --------------------------------- 

          (a)  All persons who are employees of First Savings immediately prior
to the Effective Time ("Bayonne's Employees") and whose employment is not
specifically terminated at or prior to the Effective Time (a "Continuing
Employee") shall, at the Effective Time, become employees of RCFC or RCFC Bank,
respectively; provided, however, that in no event shall any of Bayonne's
Employees be officers of RCFC or RCFC Bank, or have or exercise any power or
duty conferred upon such an officer, unless and until duly elected or appointed
to such position in accordance with the bylaws of RCFC or RCFC Bank.  Subject to
paragraph (e) of this Section 4.13, all of Bayonne's Employees who remain
following the Effective Date shall be employed at the will of RCFC or RCFC Bank
and no contractual right to employment shall inure to such employees because of
this Agreement.  Except as provided in paragraph (e) of this Section 4.13, no
employee of Bayonne will become a contractual employee of RCFC or RCFC Bank
unless such contract is in writing and executed by the President or Chief
Executive Officer of RCFC or RCFC Bank.

          (b)  Except as otherwise provided in paragraphs (c), (f) and (g) of
this Section 4.13, appropriate steps shall be taken to terminate all Bayonne
Employee Plans as of the Effective Time or as promptly as practical thereafter.
Except as provided in paragraph (c) of this Section 4.13, immediately following
the Effective Time, each Continuing Employee shall be eligible to participate in
RCFC Employee Plans, on the same basis as any newly-hired employee of RCFC or
RCFC Bank (it being understood that inclusion of Continuing Employees in RCFC
Employee Plans may occur at different times with respect to different plans);
provided, however, that with respect to each RCFC Employee Plan, other than the
Richmond County Savings Bank Employee Stock Ownership Plan (the "RCFC Bank
ESOP") and the Retirement Plan of Richmond County Savings Bank in RSI Trust (the
"RCFC Bank Retirement Plan"), for purposes of determining eligibility to
participate, vesting, and entitlement to benefits, service with Bayonne or First
Savings shall be treated as service with RCFC or RCFC Bank; provided further
however, that such service shall not be recognized to the extent such
recognition would result in a duplication of benefits.  Such service shall also
apply for purposes of satisfying any waiting periods, evidence of insurability
requirements, or the application of any preexisting condition limitation with
respect to any RCFC or RCFC Bank welfare benefit plan.  For purposes of
determining eligibility to participate, vesting, and entitlement to benefits
(including accrual of benefits) under the RCFC Bank ESOP or RCFC Bank Retirement
Plan, Continuing Employees shall be treated as newly-hired employees of RCFC or
RCFC Bank as of the Effective Date and credit for service shall begin accruing
as of that date.

          (c)  As of the Effective Time, each Bayonne Employee who is a
participant in the Bayonne 401(k) Plan (the "Bayonne 401(k) Plan") shall become
fully vested in his or her account balance in the Bayonne 401(k) Plan and the
Bayonne 401(k) Plan will either be merged into the Richmond County Savings Bank
401(k) Savings Plan (the "RCFC Bank 401(k) Plan") effective as of a date
following the Effective Time selected by RCFC Bank or, if so elected by RCFC
Bank, terminated immediately prior to, on, or after the Effective Time.  The
determination 

                                       48
<PAGE>
 
as to whether the Bayonne Savings Plan shall be terminated or merged into the
RCFC Bank 401(k) Plan shall be made by RCFC Bank. Effective as of the date of
the merger of the Bayonne 401(k) Plan into the RCFC 401(k) Plan, if applicable,
or the termination of the Bayonne 401(k) Plan (or the Effective Time, if
subsequent to such termination), if applicable, Bayonne Employees who are then
participating in the Bayonne 401(k) Plan shall become participants in the RCFC
Bank 401(k) Plan.

          (d)  RCFC agrees to honor existing employment agreements, including
the change in control provisions of such agreements, between Bayonne and First
Savings and certain employees, stock option plans and restricted stock plans,
and other benefit plans as set forth in Bayonne's Disclosure Letter
(collectively "Employment Agreements") and to the payment of benefits by Bayonne
as of the Effective Time or earlier as agreed to by Bayonne and RCFC under such
agreements and plans as described in the Bayonne Disclosure Schedule. Payments
under the Employment Agreements may be made by Bayonne if so agreed to by RCFC.

          (e)  At the Effective Time, RCFC Bank shall enter into an employment
agreement with Michael J. Nilan, substantially in the form attached hereto as
Exhibit D.

          (f)  [RESERVED]

          (g)  Immediately following execution of this Agreement, Bayonne shall
take all appropriate steps necessary to "freeze" benefit accruals under the tax-
qualified defined benefit plan sponsored by Bayonne.

          (h)  RCFC shall cause its Board of Directors to be increased by one
member and shall appoint Patrick F.X. Nilan as the nominee to fill such vacancy
on RCFC's Board of Directors created by such increase.  The term for Mr. Patrick
F.X. Nilan shall expire in the year 2000 and he shall receive only RCFC Board
fees and no Divisional Board fees during this term.

          (i)  Immediately upon execution of this Agreement, the Board of
Directors of Bayonne shall provide notice to Patrick F.X. Nilan of termination
of the consulting agreement between Bayonne and Patrick F.X. Nilan.  Such notice
of termination shall be effective as of the Effective Date.  Consideration to be
paid pursuant to the termination of the consulting agreement is to be made as
disclosed in the Bayonne Disclosure Letter.

          (j)  Upon request, Bayonne shall supply RCFC with all documentation
regarding all actions taken in accordance with this Section 4.13.

          Section 4.14.  Indemnification.
                         --------------- 

          (a)  From and after the Effective Time through the sixth anniversary
of the Effective Date, RCFC (and any successor) agrees to indemnify and hold
harmless each present and former director, officer and employee of Bayonne and
its Subsidiaries and each officer or employee of Bayonne and its Subsidiaries
that is serving or has served as a director or trustee of 

                                       49
<PAGE>
 
another entity expressly at Bayonne's request or direction (each, an
"Indemnified Party"), against any costs or expenses (including reasonable
attorneys' fees), judgments, fines, amount paid in settlement, losses, claims,
damages or liabilities (collectively, "Costs") incurred in connection with any
claim, action, suit, proceeding or investigation, whether civil, criminal,
administrative or investigative, arising out of matters existing or occurring at
or prior to the Effective Time (including the transactions contemplated by this
Agreement), whether asserted or claimed prior to, at or after the Effective
Time, and to advance any such Costs to each Indemnified Party as they are from
time to time incurred, in each case to the fullest extent such Indemnified Party
would have been indemnified as a director, officer or employee of Bayonne and
its Subsidiaries and as then permitted under the DGCL.

          (b)  Any Indemnified Party wishing to claim indemnification under
Section 4.14(a), upon learning of any such claim, action, suit, proceeding or
investigation, shall promptly notify RCFC thereof, but the failure to so notify
shall not relieve RCFC of any liability it may have hereunder to such
Indemnified Party if such failure does not materially and substantially
prejudice the indemnifying party.  In the event of any such claim, action, suit,
proceeding or investigation, (i) RCFC shall have the right to assume the defense
thereof with counsel reasonably acceptable to the Indemnified Party and RCFC
shall not be liable to such Indemnified Party for any legal expenses of other
counsel subsequently incurred by such Indemnified Party in connection with the
defense thereof, except that if RCFC does not elect to assume such defense
within a reasonable time or counsel for the Indemnified Party at any time
advises that there are issues which raise conflicts of interest between RCFC and
the Indemnified Party (and counsel for RCFC does not disagree), the Indemnified
Party may retain counsel satisfactory to such Indemnified Party, and RCFC shall
remain responsible for the reasonable fees and expenses of such counsel as set
forth above, to be paid promptly as statements therefor are received; provided,
however, that RCFC shall be obligated pursuant to this paragraph (b) to pay for
only one firm of counsel for all Indemnified Parties in any one jurisdiction
with respect to any given claim, action, suit, proceeding or investigation
unless the use of one counsel for such Indemnified Parties would present such
counsel with a conflict of interest; (ii) the Indemnified Party will reasonably
cooperate in the defense of any such matter; and (iii) RCFC shall not be liable
for any settlement effected by an Indemnified Party without its prior written
consent, which consent may not be withheld unless such settlement is
unreasonable in light of such claims, actions, suits, proceedings or
investigations against, or defenses available to, such Indemnified Party.

          (c)  RCFC shall pay all reasonable Costs, including attorneys' fees,
that may be incurred by any Indemnified Party in successfully enforcing the
indemnity and other obligations provided for in this Section 4.14 to the fullest
extent permitted under the DGCL.  The rights of each Indemnified Party hereunder
shall be in addition to any other rights such Indemnified Party may have under
applicable law.

          (d)  RCFC shall maintain Bayonne's existing directors and officers'
insurance policy (or provide a policy providing comparable coverage and amounts
on terms no less favorable to the persons currently covered by Bayonne's
existing policy, including RCFC's 

                                       50
<PAGE>
 
existing policy if its meets the foregoing standard) covering persons who are
currently covered by such insurance for a period of 3 years after the effective
date.

          (e)  In the event RCFC or any of its successors or assigns 
(i) consolidates with or merges into any other person or entity and shall not be
the continuing or surviving corporation or entity of such consolidation or
merger, or (ii) transfers or conveys all or substantially all of its properties
and assets to any person or entity, then, and in each such case, to the extent
necessary, proper provision shall be made so that the successors and assigns of
RCFC assume the obligations set forth in this Section 4.14.

          (f)  The provisions of this Section 4.14 are intended to be for the
benefit of, and shall be enforceable by, each Indemnified Party and his or her
representatives.

          Section 4.15.  Pooling and Tax-Free Reorganization Treatment.   Prior
                         ---------------------------------------------         
to the Effective Time, neither RCFC nor Bayonne shall intentionally take, fail
to take, or cause to be taken or not taken, or cause or permit any of their
respective Subsidiaries to take, fail to take, or cause to be taken or not
taken, any action within its control that would disqualify the Merger as a
pooling-of- interests for accounting purposes or as a reorganization within the
meaning of Section 368(a) of the Code.  Subsequent to the Effective Time, RCFC
shall not take any action within its control that would disqualify the Merger as
a pooling-of-interests for accounting purposes or as a reorganization under the
Code.

          Section 4.16.  Divisional Board.  RCFC shall, promptly following the
                         ----------------                                     
Effective Time, cause all of the members of Bayonne's Board of Directors as of
the date of this Agreement, who are willing to so serve, to be elected to or
appointed as members of RCFC's divisional board ("Divisional Board"), the
function of which shall be to advise RCFC with respect to deposit and lending
activities in Bayonne's market area and to maintain and develop customer
relationships. The members of the Board who are willing to so serve shall be
elected to serve a term not to exceed April 30, 2003.  Beginning immediately
after the Effective Time, each member of the Divisional Board shall receive an
annual retainer fee of $12,000 and a $1,000 attendance fee for each board
meeting attended.  Each member of the Divisional Board shall be prohibited from
competing with RCFC for the duration of the term for which they were elected or
appointed. Such Divisional Board annual retainer fee shall be payable in
quarterly installments or in one lump sum at any time in advance at the option
of RCFC.  The responsibilities and obligations of members of the Divisional
Board shall be determined by RCFC.  Service on the Divisional Board shall be
deemed to constitute service for purposes of the vesting provisions of the
Bayonne Option Plans and the Bayonne RRP.  In the event RCFC or any of its
successors or assigns (i) consolidates with or merges into any other person or
entity and shall not be the continuing or surviving corporation or entity of
such consolidation or merger, or (ii) transfers or conveys all or substantially
all of its properties and assets to any person or entity, then, and in each such
case, to the extent necessary, proper provision shall be made so that the
successors and assigns of RCFC assume the obligations set forth in this 
Section 4.16.

                                       51
<PAGE>
 
                                   ARTICLE V
                           CONDITIONS TO CONSUMMATION
                           --------------------------

          Section 5.1.   Conditions to Each Party's Obligations.  The respective
                         --------------------------------------                 
obligations of each party to effect the Merger, the Bank Merger and any other
transactions contemplated by this Agreement shall be subject to the satisfaction
of the following conditions:

          (a)  this Agreement shall have been approved by the requisite vote of
Bayonne's and RCFC's stockholders in accordance with applicable laws and
regulations;

          (b)  the Requisite Regulatory Approvals and any waivers with respect
to this Agreement and the transactions contemplated hereby shall have been
obtained and shall remain in full force and effect, and all statutory waiting
periods shall have expired; and all other consents, waivers and approvals of any
third parties which are necessary to permit the consummation of the Merger and
the other transactions contemplated hereby shall have been obtained or made
except for those the failure to obtain would not have a Material Adverse Effect
(i) on Bayonne and its Subsidiaries taken as a whole or (ii) on RCFC and its
Subsidiaries taken as a whole.  No such approval or consent shall have imposed
any condition or requirement that would so materially and adversely impact the
economic or business benefits to RCFC or Bayonne of the transactions
contemplated hereby that, had such condition or requirement been known, such
party would not, in its reasonable judgment, have entered into this Agreement.

          (c)  no party hereto shall be subject to any order, decree or
injunction of a court or agency of competent jurisdiction which enjoins or
prohibits the consummation of the Merger, the Bank Merger or any other
transactions contemplated by this Agreement;

          (d)  no statute, rule or regulation shall have been enacted, entered,
promulgated, interpreted, applied or enforced by any governmental authority
which prohibits, restricts or makes illegal consummation of the Merger, the Bank
Merger or any other transactions contemplated by this Agreement;

          (e)  the Registration Statement shall have been declared effective by
the SEC and no proceedings shall be pending or threatened by the SEC to suspend
the effectiveness of the Registration Statement; RCFC shall have received all
required approvals by state securities or "blue sky" authorities with respect to
the transactions contemplated by this Agreement;

          (f)  RCFC shall have received a letter, dated as of the Effective
Date, from its independent certified public accountants, reasonably satisfactory
to RCFC, to the effect that such auditors are not aware of any facts or
circumstances that might cause the Merger not to qualify for pooling of
interests accounting treatment;

          (g)  Bayonne shall have received a letter, dated as of the Effective
Date, from its independent certified public accountants, reasonably satisfactory
to RCFC, to the effect that 

                                       52
<PAGE>
 
such auditors are not aware of any facts and circumstances that might cause the
Merger not to qualify for pooling of interests accounting treatment; and

          (h)  RCFC shall have caused to be listed on the Nasdaq National
Market, or on such other market on which shares of RCFC Common Stock shall then
be trading, subject only to official notice of issuance, the shares of RCFC
Common Stock to be issued by RCFC in exchange for the shares of Bayonne Common
Stock.

          Section 5.2.   Conditions to the Obligations of RCFC and RCFC Bank.
                         --------------------------------------------------- 
The obligations of RCFC and RCFC Bank to effect the Merger, the Bank Merger and
any other transactions contemplated by this Agreement shall be further subject
to the satisfaction of the following additional conditions, any one or more of
which may be waived by RCFC:

          (a)  each of the obligations of Bayonne and First Savings,
respectively, required to be performed by it at or prior to the Closing pursuant
to the terms of this Agreement shall have been duly performed and complied with
in all material respects and the representations and warranties of Bayonne and
First Savings contained in this Agreement shall be true and correct, subject to
Sections 2.1 and 2.2, as of the date of this Agreement and as of the Effective
Time as though made at and as of the Effective Time (except as to any
representation or warranty which specifically relates to an earlier date).  RCFC
shall have received a certificate to the foregoing effect signed by the chief
executive officer and the chief financial or principal accounting officer of
Bayonne;

          (b)  all action required to be taken by, or on the part of, Bayonne
and First Savings to authorize the execution, delivery and performance of this
Agreement and the consummation by Bayonne and First Savings of the transactions
contemplated hereby shall have been duly and validly taken by the Board of
Directors and stockholders of Bayonne or First Savings, as the case may be, and
RCFC shall have received certified copies of the resolutions evidencing such
authorization;

          (c)  Bayonne shall have obtained the consent or approval of each
person (other than the governmental approvals or consents referred to in Section
5.1(b)) whose consent or approval shall be required in order to permit the
succession by the surviving corporation pursuant to the Merger to any
obligation, right or interest of Bayonne or its Subsidiaries under any loan or
credit agreement, note, mortgage, indenture, lease, license or other agreement
or instrument to which Bayonne or its Subsidiaries is a party or is otherwise
bound, except those for which failure to obtain such consents and approvals
would not, individually or in the aggregate, have a Material Adverse Effect on
RCFC (after giving effect to the consummation of the transactions contemplated
hereby) or upon the consummation of the transactions contemplated hereby.

          (d)  RCFC shall have received certificates (such certificates to be
dated as of a day as close as practicable to the Closing Date) from appropriate
authorities as to the corporate existence and good standing of Bayonne and its
Subsidiaries;

                                       53
<PAGE>
 
          (e)  RCFC shall have received an opinion of Muldoon, Murphy &
Faucette, counsel to RCFC, dated as of the Effective Date, in form and substance
customary in transactions of the type contemplated hereby, and reasonably
satisfactory to RCFC, substantially to the effect that on the basis of the
facts, representations and assumptions set forth in such opinion which are
consistent with the state of facts existing at the Effective Time, the Merger
will be treated for federal income tax purposes as a reorganization within the
meaning of Section 368(a) of the Code and that accordingly:

               (i)  No gain or loss will be recognized by RCFC, RCFC Bank,
Bayonne or First Savings as a result of the Merger;

               (ii)  Except to the extent of any cash received in lieu of a
fractional share interest in RCFC Common Stock, no gain or loss will be
recognized by the stockholders of Bayonne who exchange their Bayonne Common
Stock for RCFC Common Stock pursuant to the Merger;

               (iii)  The tax basis of RCFC Common Stock received by
stockholders who exchange their Bayonne Common Stock for RCFC Common Stock in
the Merger will be the same as the tax basis of Bayonne Common Stock surrendered
pursuant to the Merger, reduced by any amount allocable to a fractional share
interest for which cash is received and increased by any gain recognized on the
exchange; and

               (iv)  The holding period of RCFC Common Stock received by each
stockholder in the Merger will include the holding period of Bayonne Common
Stock exchanged therefor, provided that such stockholder held such Bayonne
Common Stock as a capital asset on the Effective Date.

          Such opinion may be based on, in addition to the review of such
matters of fact and law as Muldoon, Murphy & Faucette considers appropriate, 
(x) representations made at the request of Muldoon, Murphy & Faucette by RCFC,
RCFC Bank, Bayonne, First Savings, stockholders of RCFC or Bayonne, or any
combination of such persons and (y) certificates provided at the request of
Muldoon, Murphy & Faucette by officers of RCFC, RCFC Bank, Bayonne, First
Savings and other appropriate persons.

          Section 5.3.   Conditions to the Obligations of Bayonne and First
                         --------------------------------------------------
Savings.  The obligations of Bayonne and First Savings to effect the Merger, the
- -------                                                                         
Bank Merger and any other transactions contemplated by this Agreement shall be
further subject to the satisfaction of the following additional conditions, any
one or more of which may be waived by Bayonne:

          (a)  each of the obligations of RCFC and RCFC Bank, respectively,
required to be performed by it at or prior to the Closing pursuant to the terms
of this Agreement shall have been duly performed and complied with in all
material respects and the representations and warranties of RCFC and RCFC Bank
contained in this Agreement shall be true and correct, subject to Sections 2.1
and 2.2, as of the date of this Agreement and as of the Effective Time as 

                                       54
<PAGE>
 
though made at and as of the Effective Time (except as to any representation or
warranty which specifically relates to an earlier date). Bayonne shall have
received a certificate to the foregoing effect signed by the chief executive
officer and the chief financial or principal accounting officer of RCFC;

          (b)  all action required to be taken by, or on the part of, RCFC and
RCFC Bank to authorize the execution, delivery and performance of this Agreement
and the consummation by RCFC and RCFC Bank of the transactions contemplated
hereby shall have been duly and validly taken by the Board of Directors and
stockholders of RCFC or RCFC Bank, as the case may be, and Bayonne shall have
received certified copies of the resolutions evidencing such authorization;

          (c)  RCFC shall have obtained the consent or approval of each person
(other than the governmental approvals or consents referred to in Section
5.1(b)) whose consent or approval shall be required in connection with the
transactions contemplated hereby under any loan or credit agreement, note,
mortgage, indenture, lease, license or other agreement or instrument to which
RCFC or its Subsidiaries is a party or is otherwise bound, except those for
which failure to obtain such consents and approvals would not, individually or
in the aggregate, have a Material Adverse Effect on RCFC (after giving effect to
the transactions contemplated hereby) or upon the consummation of the
transactions contemplated hereby.

          (d)  Bayonne shall have received certificates (such certificates to be
dated as of a day as close as practicable to the Closing Date) from appropriate
authorities as to the corporate existence and good standing of RCFC and its
Subsidiaries;

          (e)  Bayonne shall have received an opinion of Breyer & Aguggia LLP,
counsel to Bayonne, dated as of the Effective Date, in form and substance
customary in transactions of the type contemplated hereby, and reasonably
satisfactory to Bayonne, substantially to the effect that on the basis of the
facts, representations and assumptions set forth in such opinion which are
consistent with the state of facts existing at the Effective Time, the Merger
will be treated for federal income tax purposes as a reorganization within the
meaning of Section 368(a) of the Code and that accordingly:

               (i)  No gain or loss will be recognized by RCFC, RCFC Bank,
Bayonne or First Savings as a result of the Merger;

               (ii)  Except to the extent of any cash received in lieu of a
fractional share interest in RCFC Common Stock, no gain or loss will be
recognized by the stockholders of Bayonne who exchange their Bayonne Common
Stock for RCFC Common Stock pursuant to the Merger;

               (iii) The tax basis of RCFC Common Stock received by
stockholders who exchange their Bayonne Common Stock for RCFC Common Stock in
the Merger will be the same as the tax basis of Bayonne Common Stock surrendered
pursuant to the Merger, 

                                       55
<PAGE>
 
reduced by any amount allocable to a fractional share interest for which cash is
received and increased by any gain recognized on the exchange; and

               (iv)  The holding period of RCFC Common Stock received by each
stockholder in the Merger will include the holding period of Bayonne Common
Stock exchanged therefor, provided that such stockholder held such Bayonne
Common Stock as a capital asset on the Effective Date.

          (f)  RCFC shall have provided to the Exchange Agent (i) certificates
representing at least the aggregate number of shares of RCFC Common Stock to be
issued to the shareholders of Bayonne pursuant to the terms hereof, and (ii)
sufficient cash to pay Bayonne shareholders their fractional share interest as
provided herein.

          Such opinion may be based on, in addition to the review of such
matters of fact and law as Breyer & Aguggia, LLP considers appropriate, (x)
representations made at the request of Breyer & Aguggia LLP by RCFC, RCFC Bank,
Bayonne, First Savings, stockholders of RCFC or Bayonne, or any combination of
such persons and (y) certificates provided at the request of Breyer & Aguggia
LLP by officers of RCFC, RCFC Bank, Bayonne and other appropriate persons.


                                   ARTICLE VI
                                  TERMINATION
                                  -----------

          Section 6.1.   Termination.   This Agreement may be terminated, and
                         -----------                                         
the Merger abandoned, at or prior to the Effective Date, either before or after
any requisite stockholder approval:

          (a)  by the mutual consent of RCFC and Bayonne in a written
instrument, if the Board of Directors of each so determines by vote of a
majority of the members of its entire Board; or

          (b)  by RCFC or Bayonne, if its Board of Directors so determines by
vote of a majority of the members of its entire Board, in the event of the
failure of the stockholders of Bayonne or RCFC to approve the Agreement at its
Stockholder Meeting called to consider such approval; provided, however, that
Bayonne or RCFC, as the case may be, shall only be entitled to terminate the
Agreement pursuant to this clause if it has complied in all material respects
with its obligations under Section 4.8; or

          (c)  by RCFC or Bayonne, by written notice to the other party, if
either (i) any approval, consent or waiver of a governmental agency required to
permit consummation of the transactions contemplated hereby shall have been
denied or (ii) any governmental authority of competent jurisdiction shall have
issued a final, unappealable order enjoining or otherwise prohibiting
consummation of the transactions contemplated by this Agreement; or

                                       56
<PAGE>
 
          (d)  by RCFC or Bayonne, if its Board of Directors so determines by
vote of a majority of the members of its entire Board, in the event that the
Merger is not consummated by April 30, 1999 ("Initial Termination Date");
provided, that if, as of such date, all necessary regulatory or governmental
approvals, consents or waivers required to consummate the transactions
contemplated hereby shall not have been obtained but all other conditions to the
consummation of the Merger (other than the delivery of executed documents at the
Closing) shall be fulfilled, the Initial Termination Date shall be extended to
July 31, 1999, unless the failure to so consummate by such time is due to the
breach of any representation, warranty or covenant contained in this Agreement
by the party seeking to terminate; or

          (e)  by RCFC, if the Board of Directors of Bayonne does not publicly
recommend in the Proxy Statement that Bayonne's stockholders approve and adopt
this Agreement or if, after recommending in the Proxy that stockholders approve
and adopt this Agreement, the Board of Directors of Bayonne shall have
withdrawn, modified or amended such recommendation in any respect materially
adverse to RCFC; or

          (f)  by RCFC or Bayonne by written notice to the other party in the
event that there has occurred since the date of this Agreement an event,
condition, change or occurrence which, individually or in the aggregate, has had
or could reasonably be expected to result in a Material Adverse Effect on
Bayonne or RCFC as the case may be; provided that each party shall have given
the other 30 calendar days prior written notice of such termination, and such
party shall not have remedied such event, condition, change or occurrence by the
end of such 30-day period;

          (g)  by Bayonne, if its Board of Directors so determines by the
requisite vote of members of its entire board, at any time during the 5-day
period commencing with the Valuation Date, if both of the following conditions
are satisfied:

               (i) Richmond Market Value is less than $15.41, adjusted as
          indicated in the last sentence of this Section 6.1(g); and

               (ii) (A) the number obtained by dividing Richmond Market Value on
          such Valuation Date by the Initial RCFC Market Value (the "Richmond
          Ratio") is less than (B) the number obtained by dividing the Final
          Index Price by the Initial Index Price and subtracting 0.15 from the
          quotient in this clause (ii)(B) (the "Index Ratio");

subject, however, to the following three sentences: (1) if Bayonne elects to
exercise its termination right pursuant to this Section 6.1(g), it shall give
prompt written notice to Richmond (provided, further, that such notice of
election to terminate may be withdrawn at any time during the 5-day period); (2)
for a period of 7 days commencing with its receipt of such notice, RCFC shall
have the option to increase the consideration to be received by the holders of
Bayonne 

                                       57
<PAGE>
 
Common Stock hereunder, by adjusting the Exchange Ratio to equal the lesser of
(x) a number equal to a fraction, the numerator of which is 1.05 multiplied by
the Initial RCFC Market Value multiplied by .85 and the denominator of which is
the Richmond Market Value, and (y) a number equal to a fraction, the numerator
of which is the Index Ratio multiplied by 1.05 and the denominator of which is
Richmond Ratio; and (3) if RCFC so elects it shall give prompt written notice to
Bayonne of such election and the adjusted Merger Consideration, whereupon no
termination shall have occurred pursuant to this Section 6.1(g) and this
Agreement shall remain in effect in accordance with its terms (except as the
Merger Consideration shall have been so adjusted).

     For purposes of this Section 6.1(g), the following terms shall have the
meanings indicated below:

          "Final Index Price" means the sum of the Final Prices for each company
     comprising the Index Group multiplied by the applicable weighting.

          "Final Price," with respect to any company being a member of the Index
     Group, means the average of the daily closing sales prices of a share of
     common stock of such company, as reported on the consolidated transaction
     reporting system for the market or exchange on which such common stock is
     principally traded, during the period of 15 trading days ending on the
     Valuation Date, adjusted as indicated in the last sentence of this Section
     6.1(g).

          "Index Group" means the 14 financial institution holding companies
     listed below, the common stock of all of which are publicly traded and as
     to which there have not been any publicly announced proposal at any time
     during the period beginning on the date of this Agreement and ending on the
     Valuation Date for any such company to be acquired. In the event that the
     common stock of any such company ceases to be publicly traded or a proposal
     to acquire any such company is announced at any time during the period
     beginning on the date of this Agreement and ending on the Valuation Date,
     such company shall be removed from the Index Group, and the weights
     attributed to the remaining companies shall be adjusted proportionately for
     purposes of determining the Final Index Price and the Initial Index Price.
     The 14 financial institution holding companies and the weights attributed
     to them are as follows:

<TABLE> 
<CAPTION> 
          Holding Company                      Weighting
          ---------------                      ---------
          <S>                                  <C>
          GreenPoint Financial Corp.             27.71%
          Astoria Financial Corp.                11.20%
          Independence Community Bank Corp.       9.97%
          Staten Island Bancorp, Inc.             8.14%
          Webster Financial Corp.                 7.16%
          St. Paul Bancorp, Inc.                  6.61%
          Queens County Bancorp, Inc.             5.13%
</TABLE> 

                                       58
<PAGE>
 
<TABLE> 
<CAPTION> 
          Holding Company                      Weighting
          ---------------                      ---------
          <S>                                  <C>
          Bay View Capital Corp.                  4.96%
          JSB Financial, Inc.                     4.52%
          MAF Bancorp                             4.24%
          Anchor BanCorp Wisconsin                3.03%
          InterWest Bancorp                       2.88%
          Reliance Bancorp, Inc.                  2.76%
          Haven Bancorp, Inc.                     1.69%
</TABLE> 

          "Initial Index Price" means the sum of each per share closing price of
     the common stock of each company comprising the Index Group multiplied by
     the applicable weighting, as such prices are reported on the consolidated
     transactions reporting system for the market or exchange on which such
     common stock is principally traded on the trading day immediately preceding
     the public announcement of this Agreement.

          "Initial RCFC Market Value" means the closing sales price of RCFC
     Common Stock, as reported on the Nasdaq National Market, on the trading day
     immediately preceding the public announcement of this Agreement, adjusted
     as indicated in the last Section 6.1(e).

          "Richmond Market Value" shall have the meaning set forth in Section
     1.2(c) hereof.

          "Valuation Date" means the Valuation Date, as defined in Section
     1.2(c) hereof.

If RCFC or any company belonging to the Index Group declares or effects a stock
dividend, reclassification, recapitalization, split-up, combination, exchange of
shares or similar transaction between the date of this Agreement and the
Valuation Date, the prices for the common stock of such company shall be
appropriately adjusted, in the manner specified in Section 1.2(b) of this
Agreement, for the purposes of applying this Section 6.1(g).

          (h)  by RCFC or Bayonne (provided that the party seeking termination
is not then in material breach of any representation, warranty, covenant or
other agreement contained herein), in the event of (i) a failure to perform or
comply by the other party with any covenant or agreement of such other party
contained in this Agreement, which failure or non-compliance is material in the
context of the transactions contemplated by this Agreement, or (ii) subject to
Section 2.2(b), any inaccuracies, omissions or breach in the representations,
warranties, covenants or agreements of the other party contained in this
Agreement the circumstances as to which either individually or in the aggregate
have, or reasonably could be expected to have, a Material Adverse Effect on such
other party; in either case which has not been or cannot be cured within 30
calendar days after written notice thereof is given by the party seeking to
terminate to such other party.

                                       59
<PAGE>
 
          (i)  by Bayonne, if the Board of Directors of RCFC does not publicly
recommend in the Proxy Statement-Prospectus that RCFC's stockholders approve and
adopt this Agreement or if, after recommending in the Proxy Statement-Prospectus
that stockholders approve and adopt this Agreement, the Board of Directors of
RCFC shall have withdrawn, modified or amended such recommendation in any
respect materially adverse to Bayonne.

          (j)  by Bayonne, if the Board of Directors of Bayonne reasonably
determines that a proposal made by a third party to acquire, directly or
indirectly, including pursuant to a tender offer, exchange offer, merger,
consolidation, business combination, recapitalization, liquidation, dissolution
or similar transaction, for consideration consisting of cash and/or securities,
more than 65% of the combined voting power of the shares of Bayonne Common Stock
then outstanding or all or substantially all of the assets of Bayonne
constitutes a Superior Proposal and that such proposal must be accepted;
provided, however, that prior to any such termination, Bayonne shall use its
reasonable efforts to negotiate in good faith with RCFC to make such adjustments
in the terms and conditions of this agreement a would enable Bayonne to proceed
with the transactions contemplated herein.

          Section 6.2.   Effect of Termination.  In the event of termination of
                         ---------------------                                 
this Agreement by either RCFC or Bayonne as provided in Section 6.1, this
Agreement shall forthwith become void and have no effect except (i) Sections
4.3(a), 8.6 and 8.7, shall survive any termination of this Agreement, (ii) that
notwithstanding anything to the contrary contained in this Agreement, no party
shall be relieved or released from any liabilities or damages arising out of its
willful breach of any provision of this Agreement.


                                  ARTICLE VII
                   CLOSING, EFFECTIVE DATE AND EFFECTIVE TIME
                   ------------------------------------------

          Section 7.1.   Effective Date and Effective Time.  The closing of the
                         ---------------------------------                     
transactions contemplated hereby ("Closing") shall take place at the offices of
Muldoon, Murphy & Faucette, 5101 Wisconsin Ave. N.W., Washington, D.C.  20016,
unless another place is agreed to by RCFC and Bayonne, on a date ("Closing
Date") that is no later than 14 days following the date on which the expiration
of the last applicable waiting period in connection with notices to and
approvals of governmental authorities shall occur and all conditions to the
consummation of this Agreement are satisfied or waived, or on such other date as
may be agreed to by the parties. Prior to the Closing Date, RCFC and Bayonne
shall execute a Certificate of Merger in accordance with all appropriate legal
requirements, which shall be filed as required by law on the Closing Date, and
the Merger provided for therein shall become effective upon such filing or on
such date as may be specified in such Certificate of Merger.  The date of such
filing or such later effective date as specified in the Certificate of Merger is
herein referred to as the "Effective Date."  The "Effective Time" of the Merger
shall be as set forth in the Certificate of Merger.

                                       60
<PAGE>
 
          Section 7.2.   Deliveries at the Closing.   Subject to the provisions
                         -------------------------                             
of Articles V and VI, on the Closing Date there shall be delivered to RCFC and
Bayonne the documents and instruments required to be delivered under Article V.


                                  ARTICLE VIII
                             CERTAIN OTHER MATTERS
                             ---------------------

          Section 8.1.   Certain Definitions; Interpretation.   As used in this
                         -----------------------------------                   
Agreement, the following terms shall have the meanings indicated:

          "material" means material to RCFC or Bayonne (as the case may be) and
     its respective Subsidiaries, taken as a whole.

          "person" includes an individual, corporation, limited liability
     company, partnership, association, trust or unincorporated organization.

          When a reference is made in this Agreement to Sections, Exhibits or
Schedules, such reference shall be to a Section of, Exhibit or Schedule to, this
Agreement unless otherwise indicated.  The table of contents and headings
contained in this Agreement are for ease of reference only and shall not affect
the meaning or interpretation of this Agreement.  Whenever the words "include,"
"includes" or "including" are used in this Agreement, they shall be deemed
followed by the words "without limitation."  Any singular term in this Agreement
shall be deemed to include the plural, and any plural term the singular.  Any
reference to gender in this Agreement shall be deemed to include any other
gender.

          Section 8.2.   Survival.   Only those agreements and covenants of the
                         --------                                              
parties that are by their terms applicable in whole or in part after the
Effective Time, including Sections 4.3(a), 4.13,  4.14, 4.15, 4.16 and 8.6 of
this Agreement, shall survive the Effective Time.  All other representations,
warranties, agreements and covenants shall be deemed to be conditions of the
Agreement and shall not survive the Effective Time.

          Section 8.3.   Waiver; Amendment.   Prior to the Effective Time, any
                         -----------------                                    
provision of this Agreement may be: (i) waived in writing by the party
benefitted by the provision or (ii) amended or modified at any time (including
the structure of the transaction) by an agreement in writing between the parties
hereto except that, after the vote by the stockholders of Bayonne or RCFC, no
amendment or modification may be made that would reduce the amount or alter or
change the kind of consideration to be received by holders of Bayonne Common
Stock or contravene any provision of the DGCL or the federal banking laws, rules
and regulations.

          Section 8.4.   Counterparts.   This Agreement may be executed in
                         ------------                                     
counterparts each of which shall be deemed to constitute an original, but all of
which together shall constitute one and the same instrument.

                                       61
<PAGE>
 
          Section 8.5.   Governing Law.   This Agreement shall be governed by,
                         -------------                                        
and interpreted in accordance with, the laws of the State of New York, without
regard to conflicts of laws principles.

          Section 8.6.   Expenses.   Each party hereto will bear all expenses
                         --------                                            
incurred by it in connection with this Agreement and the transactions
contemplated hereby; provided, however, that RCFC shall pay all printing and
mailing expenses and filing fees associated with the registrations and approvals
required hereunder.

          Section 8.7.   Notices.   All notices, requests, acknowledgments and
                         -------                                              
other communications hereunder to a party shall be in writing and shall be
deemed to have been duly given when delivered by hand, overnight courier or
facsimile transmission (confirmed in writing) to such party at its address or
facsimile number set forth below or such other address or facsimile transmission
as such party may specify by notice (in accordance with this provision) to the
other party hereto.

          If to Bayonne, to:

                    Bayonne Bancshares, Inc.
                    586 Broadway
                    Bayonne, New Jersey 07002
                    Facsimile:  (201) 437-2912

                    Attention:  Patrick F.X. Nilan
                                Chairman of the Board

          With copies to:

                    Bayonne Bancshares, Inc.
                    586 Broadway
                    Bayonne, New Jersey 07002
                    Facsimile:  (201) 437-5958

                    Attention:  Thomas M. Coughlin
                                Corporate Secretary

          and

                    Paul M. Aguggia, Esq.
                    Breyer & Aguggia LLP
                    1300 I Street, N.W., Suite 470 East
                    Washington, DC  20005
                    Facsimile:  (201) (737-7979)

                                       62
<PAGE>
 
          If to RCFC, to:

                    Richmond County Financial Corp.
                    1214 Castleton Avenue
                    Staten Island, New York  10310
                    Facsimile:  (718) 390-0224

                    Attention:  Michael F. Manzulli
                                Chairman of the Board and
                                  Chief Executive Officer

          With copies to:

                    Richmond County Financial Corp.
                    1214 Castleton Avenue
                    Staten Island, New York  10310
                    Facsimile:  (718) 390-0224

                    Attention:  Thomas R. Cangemi
                                Senior Vice President, Chief Financial
                                  Officer and Secretary

          and

                    Douglas P. Faucette, Esq.
                    Muldoon, Murphy & Faucette
                    5101 Wisconsin Avenue, N.W.
                    Washington, D.C.  20016
                    Facsimile: (202) 966-9409


          Section 8.8.   Entire Agreement; etc.   This Agreement, together with
                         ---------------------                                 
the Plan of Bank Merger, Option Agreement and the Disclosure Letters, represents
the entire understanding of the parties hereto with reference to the
transactions contemplated hereby and supersedes any and all other oral or
written agreements heretofore made. All terms and provisions of this Agreement
shall be binding upon and shall inure to the benefit of the parties hereto and
their respective successors and assigns.  Except for Section 4.13, 4.14 and
4.16, which confer rights on the parties described therein, nothing in this
Agreement is intended to confer upon any other person any rights or remedies of
any nature whatsoever under or by reason of this Agreement.

          Section 8.9.   Assignment.   This Agreement may not be assigned by
                         ----------                                         
either party hereto without the written consent of the other party.

                                       63
<PAGE>
 
          IN WITNESS WHEREOF, the parties hereto have caused this Agreement to
be executed by their duly authorized officers as of the 19/th/ day of July,
1998.

                            RICHMOND COUNTY FINANCIAL CORP.


                            By: /s/ Michael F. Manzulli
                                -----------------------------------
                                Michael F. Manzulli
                                Chairman of the Board and
                                   Chief Executive Officer


                            BAYONNE BANCSHARES, INC.


                            By: /s/ Patrick F.X. Nilan
                                --------------------------------------
                                Patrick F.X. Nilan
                                Chairman of the Board

                                       64

<PAGE>
 
                                                                    EXHIBIT 10.1

                             STOCK OPTION AGREEMENT

     STOCK OPTION AGREEMENT, dated as of July 19, 1998 (the "Agreement"), by and
between Bayonne Bancshares, Inc., a Delaware corporation ("Issuer"), and
Richmond County Financial Corp., a Delaware corporation ("Grantee").

     WHEREAS, Grantee and Issuer have entered into an Agreement and Plan of
Merger dated as of July 19, 1998 (the "Plan"), providing for, among other
things, the merger of Issuer with and into Grantee, with Grantee as the
surviving corporation; and

     WHEREAS, as a condition and inducement to Grantee's execution of the Plan,
Grantee has required that Issuer agree, and Issuer has agreed, to grant Grantee
the Option (as defined below);

     NOW, THEREFORE, in consideration of the foregoing and the respective
representations, warranties, covenants and agreements set forth herein and in
the Plan, and intending to be legally bound hereby, Issuer and Grantee agree as
follows:

     1.   DEFINED TERMS.  Capitalized terms which are used but not defined
herein shall have the meanings ascribed to such terms in the Plan.

     2.   GRANT OF OPTION.  Subject to the terms and conditions set forth
herein, Issuer hereby grants to Grantee an irrevocable option (the "Option") to
purchase up to 1,809,804 shares (as adjusted as set forth herein, the "Option
Shares", which shall include the Option Shares before and after any transfer of
such Option Shares) of common stock, par value $0.01 per share ("Issuer Common
Stock"), of Issuer at a purchase price per Option Share (the "Purchase Price")
equal to $15.50.

     3.   EXERCISE OF OPTION.

     (a) Provided that (i) Grantee or Holder (as defined below), as applicable,
shall not be in material breach of the agreements or covenants contained in this
Agreement or the Plan, and (ii) no preliminary or permanent injunction or other
order against the delivery of shares covered by the Option issued by any court
of competent jurisdiction in the United States shall be in effect, the Holder
may exercise the Option, in whole or in part, at any time and from time to time
following the occurrence of a Purchase Event (as hereinafter defined); PROVIDED
that the Option shall terminate and be of no further force and effect upon the
earliest to occur of (A) the Effective Time, (B) termination of the Plan by
Issuer in accordance with the terms thereof prior to the occurrence of a
Purchase Event or a Preliminary Purchase Event (as hereinafter defined) (an
"Issuer Termination"), (C) 12 months after the termination of the Plan by Issuer
other than pursuant to an Issuer Termination, (D) 12 months after the
termination of the Plan by Grantee in 

                                      E-1
<PAGE>
 
accordance with the terms thereof, and (E) 12 months after the first occurrence
of a Purchase Event; PROVIDED, HOWEVER, that any purchase of shares upon
exercise of the Option shall be subject to compliance with applicable law,
including, without limitation, the Home Owners' Loan Act, as amended (the
"HOLA"); provided, further, however, that if the option cannot be exercised on
any day because of an injunction, order or similar restraint issued by a court
of competent jurisdiction, the period during which the option may be exercised
shall be extended so that the option shall expire no earlier than the tenth
business day after such injunction, order or restraint shall have been dissolved
or when such injunction, order or restraint shall have become permanent and no
longer subject to appeal, as the case may be. The term "Holder" shall mean the
holder or holders of the Option from time to time, and which initially is
Grantee.
 
     (b) As used herein, a "Purchase Event" means any of the following events:

          (i) Without Grantee's prior written consent, Issuer shall have
     authorized, recommended, publicly proposed or publicly announced an
     intention to authorize, recommend or propose, or entered into an agreement
     with any person (other than Grantee or any subsidiary of Grantee) to effect
     an Acquisition Transaction. As used herein, the term "Acquisition
     Transaction" shall mean (A) a merger, consolidation or similar transaction
     involving Issuer or any of its significant subsidiaries, (B) the
     disposition, by sale, lease, exchange or otherwise, of assets or deposits
     of Issuer or any of its significant subsidiaries representing in either
     case 20% or more of the consolidated assets or deposits of Issuer and its
     subsidiaries, or (C) the issuance, sale or other disposition of (including
     by way of merger, consolidation, share exchange or any similar transaction)
     securities representing 15% or more of the voting power of Issuer or any of
     its significant subsidiaries other than the issuance of Issuer Common Stock
     upon the exercise of outstanding options; or

          (ii) any person (other than Grantee or any subsidiary of Grantee)
     shall have acquired beneficial ownership (as such term is defined in Rule
     13d-3 promulgated under the Exchange Act) of or the right to acquire
     beneficial ownership of, or any "group" (as such term is defined under the
     Exchange Act) shall have been formed which beneficially owns or has the
     right to acquire beneficial ownership of, 15% or more of the voting power
     of Issuer or any of its significant subsidiaries.

     (c) As used herein, a "Preliminary Purchase Event" means any of the
following events:

          (i) any person (other than Grantee or any subsidiary of Grantee) shall
     have commenced (as such term is defined in Rule 14d-2 under the Exchange
     Act), or shall have filed a registration statement under the Securities Act
     with respect to, a tender offer or exchange offer to purchase any shares of
     Issuer Common Stock such that, upon consummation of such offer, such person
     would own or control 15% or more of the then outstanding shares of Issuer
     Common Stock (such an offer being referred to herein as a "Tender Offer" or
     an "Exchange Offer," respectively); or

                                      E-2
<PAGE>
 
          (ii) the holders of Issuer Common Stock shall not have approved the
     Plan at the Meeting, the Meeting shall not have been held or shall have
     been canceled prior to termination of the Plan, or Issuer's Board of
     Directors shall have withdrawn or modified in a manner adverse to Grantee
     the recommendation of Issuer's Board of Directors with respect to the Plan,
     in each case after it shall have been publicly announced that any person
     (other than Grantee or any subsidiary of Grantee) shall have (A) made or
     disclosed an intention to make a proposal to engage in an Acquisition
     Transaction, or (B) commenced a Tender Offer or filed a registration
     statement under the Securities Act with respect to an Exchange Offer; or

          (iii)  any person, other than Grantee or any subsidiary of Grantee,
     shall have made a bona fide proposal to Issuer or its stockholders by
     public announcement, or written communication that is or becomes the
     subject of public disclosure, to engage in an Acquisition Transaction; or

          (iv) after a bona fide proposal is made by a third party to Issuer or
     its stockholders to engage in an Acquisition Transaction, Issuer shall have
     breached any covenant or obligation contained in the Plan and such breach
     would entitle Grantee to terminate the Plan under Section 6.1(h) thereof
     (without regard to the cure period provided for therein unless such cure is
     promptly effected without jeopardizing consummation of the Mergers pursuant
     to the terms of the Plan); or

          (v) any person, other than Grantee or any subsidiary of Grantee, other
     than in connection with a transaction to which Grantee has given its prior
     written consent, shall have filed an application or notice with the Office
     of Thrift Supervision (the "OTS"), or other federal or state bank
     regulatory authority, for approval to engage in an Acquisition Transaction.

          As used in this Agreement, "person" shall have the meaning specified
in Sections 3(a)(9) and 13(d)(3) of the Exchange Act.

     (d) Issuer shall notify Grantee promptly in writing of the occurrence of
any Preliminary Purchase Event or Purchase Event (in either case, a "Triggering
Event"), it being understood that the giving of such notice by Issuer shall not
be a condition to the right of Holder to exercise the Option.

     (e) In the event Holder wishes to exercise the Option, it shall send to
Issuer a written notice (the date of which being herein referred to as the
"Notice Date") specifying (i) the total number of Option Shares it intends to
purchase pursuant to such exercise, and (ii) a place and date not earlier than
three business days nor later than 15 business days from the Notice Date for the
closing (the "Closing") of such purchase (the "Closing Date"); PROVIDED,
HOWEVER, if any required application for listing such shares on the Nasdaq
National Market has not been approved by the date so specified, such date shall
be extended for a period not to exceed 21 days from the 

                                      E-3
<PAGE>
 
Notice Date. If prior notification to or approval of the OTS or any other
regulatory authority is required in connection with such purchase, Issuer shall
cooperate with the Holder in the filing of the required notice or application
for approval and the obtaining of such approval and the Closing shall occur
immediately following such regulatory approvals (and any mandatory waiting
periods). Any exercise of the Option shall be deemed to occur on the Notice Date
relating thereto.

     4.   PAYMENT AND DELIVERY OF CERTIFICATES.
 
     (a) On each Closing Date, Holder shall (i) pay to Issuer, in immediately
available funds by wire transfer to a bank account designated by Issuer, an
amount equal to the Purchase Price multiplied by the number of Option Shares to
be purchased on such Closing Date, and (ii) present and surrender this Agreement
to the Issuer at the address of the Issuer specified in subsection (f) of
Section 11 hereof.

     (b) At each Closing, simultaneously with the delivery of immediately
available funds and surrender of this Agreement as provided in subsection (a) of
this Section 4, (i) Issuer shall deliver to Holder (A) a certificate or
certificates representing the Option Shares to be purchased at such Closing,
which Option Shares shall be free and clear of all liens, claims, charges and
encumbrances of any kind whatsoever and subject to no preemptive rights, and (B)
if the Option is exercised in part only, an executed new agreement with the same
terms as this Agreement evidencing the right to purchase the balance of the
shares of Issuer Common Stock purchasable hereunder, and (ii) Holder shall
deliver to Issuer a letter agreeing that Holder shall not offer to sell or
otherwise dispose of such Option Shares in violation of applicable federal and
state law or of the provisions of this Agreement.

     (c) In addition to any other legend that is required by applicable law,
certificates for the Option Shares delivered at each Closing shall be endorsed
with a restrictive legend which shall read substantially as follows:

     THE TRANSFER OF THE STOCK REPRESENTED BY THIS CERTIFICATE IS SUBJECT TO
RESTRICTIONS ARISING UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND PURSUANT
TO THE TERMS OF A STOCK OPTION AGREEMENT DATED AS OF JULY 19, 1998. A COPY OF
SUCH AGREEMENT WILL BE PROVIDED TO THE HOLDER HEREOF WITHOUT CHARGE UPON RECEIPT
BY THE ISSUER OF A WRITTEN REQUEST THEREFOR.

     It is understood and agreed that the above legend shall be removed by
delivery of substitute certificate(s) without such legend if Holder shall have
delivered to Issuer a copy of a letter from the staff of the SEC, or an opinion
of counsel in form and substance reasonably satisfactory to Issuer and its
counsel, to the effect that such legend is not required for purposes of the
Securities Act.

                                      E-4
<PAGE>
 
     (d) Upon the giving by Holder to Issuer of the written notice of exercise
of the Option provided for under subsection (e) of Section 3 hereof, the tender
of the applicable purchase price in immediately available funds and the tender
of this Agreement to Issuer, Holder shall be deemed to be the holder of record
of the shares of Issuer Common Stock issuable upon such exercise,
notwithstanding that the stock transfer books of Issuer shall then be closed or
that certificates representing such shares of Issuer Common Stock shall not then
be actually delivered to Holder. Issuer shall pay all expenses, and any and all
United States federal, state, and local taxes and other charges that may be
payable in connection with the preparation, issuance and delivery of stock
certificates under this Section in the name of Holder or its assignee,
transferee, or designee.

     (e) Issuer agrees (i) that it shall at all times maintain, free from
preemptive rights, sufficient authorized but unissued or treasury shares of
Issuer Common Stock so that the Option may be exercised without additional
authorization of Issuer Common Stock after giving effect to all other options,
warrants, convertible securities and other rights to purchase Issuer Common
Stock, (ii) that it will not, by charter amendment or through reorganization,
consolidation, merger, dissolution or sale of assets, or by any other voluntary
act, avoid or seek to avoid the observance or performance of any of the
covenants, stipulations or conditions to be observed or performed hereunder by
Issuer, (iii) promptly to take all action as may from time to time be required
(including (A) complying with all premerger notification, reporting and waiting
period requirements specified in 15 U.S.C. (S)18a and regulations promulgated
thereunder and (B) in the event, under the HOLA, or the Change in Bank Control
Act of 1978, as amended, or a state banking law, prior approval of or notice to
the OTS or to any state regulatory authority is necessary before the Option may
be exercised, cooperating fully with Holder in preparing such applications or
notices and providing such information to the OTS or such state regulatory
authority as they may require) in order to permit Holder to exercise the Option
and Issuer duly and effectively to issue shares of the Issuer Common Stock
pursuant hereto, and (iv) promptly to take all action provided herein to protect
the rights of Holder against dilution.

     5.   REPRESENTATIONS AND WARRANTIES OF ISSUER.  Issuer hereby represents
and warrants to Grantee (and Holder, if different than Grantee) as follows:

     (a) Due Authorization.  Issuer has all requisite corporate power and
         -----------------                                               
authority to enter into this Agreement and, subject to any approvals or consents
referred to herein, to consummate the transactions contemplated hereby. The
execution and delivery of this Agreement and the consummation of the
transactions contemplated hereby have been duly authorized by all necessary
corporate action on the part of Issuer. This Agreement has been duly executed
and delivered by Issuer.

     (b) Authorized Stock.  Issuer has taken all necessary corporate and other
         ----------------                                                     
action to authorize and reserve and to permit it to issue, and, at all times
from the date hereof until the obligation to deliver Issuer Common Stock upon
the exercise of the Option terminates, will have reserved for issuance, upon
exercise of the Option, the number of shares of Issuer Common Stock necessary
for Holder to exercise the Option, and Issuer will take all necessary corporate
action to 

                                      E-5
<PAGE>
 
authorize and reserve for issuance all additional shares of Issuer Common Stock
or other securities which may be issued pursuant to Section 7 upon exercise of
the Option. The shares of Issuer Common Stock to be issued upon due exercise of
the Option, including all additional shares of Issuer Common Stock or other
securities which may be issuable pursuant to Section 7, upon issuance pursuant
hereto, shall be duly and validly issued, fully paid and nonassessable, and
shall be delivered free and clear of all liens, claims, charges and encumbrances
of any kind or nature whatsoever, including any preemptive rights of any
stockholder of Issuer.

     (c)  No Violations.  The execution, delivery and performance of this
          -------------                                                  
Agreement does not and will not, and the consummation by Issuer of any of the
transactions contemplated hereby will not, constitute or result in (i) a breach
or violation of, or a default under, its Certificate of Incorporation or By-
Laws, or the comparable governing instruments of any of its subsidiaries, or
(ii) a breach or violation of, or a default under, any agreement, lease,
contract, note, mortgage, indenture, arrangement or other obligation of it or
any of its subsidiaries (with or without the giving of notice, the lapse of time
or both) or under any law, rule, ordinance or regulation or judgment, degree,
order, award or governmental or non-governmental permit or license to which it
or any of its subsidiaries is subject, that would, in any case, give any other
person the ability to prevent or enjoin Issuer's performance under this
Agreement in any material respect.

     6.   REPRESENTATIONS AND WARRANTIES OF GRANTEE.  Grantee hereby represents
and warrants to Issuer that:

     (a) Due Authorization.  Grantee has all requisite corporate power and
         -----------------                                                
authority to enter into this Agreement and, subject to any approvals or consents
referred to herein, to consummate the transactions contemplated hereby. The
execution and delivery of this Agreement and the consummation of the
transactions contemplated hereby have been duly authorized by all necessary
corporate action on the part of Grantee. This Agreement has been duly executed
and delivered by Grantee.

     (b) Purchase not for Distribution.  This Option is not being, and any
         -----------------------------                                    
Option Shares or other securities acquired by Grantee upon exercise of the
Option will not be, acquired with a view to the public distribution thereof and
will not be transferred or otherwise disposed of except in a transaction
registered or exempt from registration under the Securities Act.

     7.   ADJUSTMENT UPON CHANGES IN ISSUER CAPITALIZATION, ETC.

     (a) In the event of any change in Issuer Common Stock by reason of a stock
dividend, stock split, split-up, recapitalization, combination, exchange of
shares or similar transaction, the type and number of shares or securities
subject to the Option, and the Purchase Price therefor, shall be adjusted
appropriately, and proper provision shall be made in the agreements governing
such transaction so that Holder shall receive, upon exercise of the Option, the
number and class of shares or other securities or property that Holder would
have received in respect of Issuer Common Stock if the Option had been exercised
immediately prior to such event, or the record 

                                      E-6
<PAGE>
 
date therefor, as applicable. If any additional shares of Issuer Common Stock
are issued after the date of this Agreement (other than pursuant to an event
described in the first sentence of this subsection (a), upon exercise of any
option to purchase Issuer Common Stock outstanding on the date hereof or upon
conversion into Issuer Common Stock of any convertible security of Issuer
outstanding on the date hereof), the number of shares of Issuer Common Stock
subject to the Option shall be adjusted so that, after such issuance, it,
together with any shares of Issuer Common Stock previously issued pursuant
hereto, equals 19.9% of the number of shares of Issuer Common Stock then issued
and outstanding, without giving effect to any shares subject to or issued
pursuant to the Option. No provision of this Section 7 shall be deemed to affect
or change, or constitute authorization for any violation of, any of the
covenants or representations in the Plan.

     (b) In the event that Issuer shall enter in an agreement (i) to consolidate
with or merge into any person, other than Grantee or one of its subsidiaries,
and shall not be the continuing or surviving corporation of such consolidation
or merger, (ii) to permit any person, other than Grantee or one of its
subsidiaries, to merge into Issuer and Issuer shall be the continuing or
surviving corporation, but, in connection with such merger, the then outstanding
shares of Issuer Common Stock shall be changed into or exchanged for stock or
other securities of Issuer or any other person or cash or any other property or
the outstanding shares of Issuer Common Stock immediately prior to such merger
shall after such merger represent less than 50% of the outstanding shares and
share equivalents of the merged company, or (iii) to sell or otherwise transfer
all or substantially all of its assets to any person, other than Grantee or one
of its subsidiaries, then, and in each such case, the agreement governing such
transaction shall make proper provisions so that the Option shall, upon the
consummation of any such transaction and upon the terms and conditions set forth
herein, be converted into, or exchanged for, an option (the "Substitute
Option"), at the election of Holder, of either (x) the Acquiring Corporation (as
hereinafter defined), (y) any person that controls the Acquiring Corporation, or
(z) in the case of a merger described in clause (ii), Issuer (such person being
referred to as "Substitute Option Issuer").

     (c) The Substitute Option shall have the same terms as the Option,
provided, that, if the terms of the Substitute Option cannot, for legal reasons,
be the same as the Option, such terms shall be as similar as possible and in no
event less advantageous to Holder. Substitute Option Issuer shall also enter
into an agreement with Holder in substantially the same form as this Agreement,
which shall be applicable to the Substitute Option.

     (d) The Substitute Option shall be exercisable for such number of shares of
Substitute Common Stock (as hereinafter defined) as is equal to the Assigned
Value (as hereinafter defined) multiplied by the number of shares of Issuer
Common Stock for which the Option was theretofore exercisable, divided by the
Average Price (as hereinafter defined). The exercise price of Substitute Option
per share of Substitute Common Stock (the "Substitute Option Price") shall then
be equal to the Option Price multiplied by a fraction in which the numerator is
the number of shares of Issuer Common Stock for which the Option was theretofore
exercisable and the denominator is 

                                      E-7
<PAGE>
 
the number of shares of the Substitute Common Stock for which the Substitute
Option is exercisable.

     (e) The following terms have the meanings indicated:

          (1) "Acquiring Corporation" shall mean (i) the continuing or surviving
          corporation of a consolidation or merger with Issuer (if other than
          Issuer), (ii) Issuer in a merger in which Issuer is the continuing or
          surviving person, or (iii) the transferee of all or substantially all
          of Issuer's assets (or a substantial part of the assets of its
          subsidiaries taken as a whole).

          (2) "Substitute Common Stock" shall mean the common stock issued by
          Substitute Option Issuer upon exercise of the Substitute Option.

          (3) "Assigned Value" shall mean the highest of (x) the price per share
          of Issuer Common Stock at which a Tender Offer or an Exchange Offer
          therefor has been made, (y) the price per share of Issuer Common Stock
          to be paid by any third party pursuant to an agreement with Issuer,
          and (z) the highest per share closing price for shares of Issuer
          Common Stock within the six-month period immediately preceding the
          consolidation, merger, or sale in question. In the event that a Tender
          Offer or an Exchange Offer is made for Issuer Common Stock or an
          agreement is entered into for a merger or consolidation involving
          consideration other than cash, the value of the securities or other
          property issuable or deliverable in exchange for Issuer Common Stock
          shall be determined by a nationally recognized investment banking firm
          selected by Holder or Owner, as the case may be (and if there are both
          a Holder and an Owner, the Holder).

          (4) "Average Price" shall mean the average closing price per share of
          Substitute Common Stock for the one year immediately preceding the
          consolidation, merger, or sale in question, but in no event higher
          than the closing price of the shares of Substitute Common Stock on the
          day preceding such consolidation, merger or sale; provided that if
          Issuer is the issuer of the Substitute Option, the Average Price shall
          be computed with respect to a share of common stock issued by Issuer,
          the person merging into Issuer or by any company which controls such
          person, as Holder may elect.

                                      E-8
<PAGE>
 
     (f) In no event, pursuant to any of the foregoing paragraphs, shall the
Substitute Option be exercisable for more than 19.9% of the aggregate of the
shares of Substitute Common Stock outstanding prior to exercise of the
Substitute Option. In the event that the Substitute Option would be exercisable
for more than 19.9% of the aggregate of the shares of Substitute Common Stock
but for the limitation in the first sentence of this subsection (f), Substitute
Option Issuer shall make a cash payment to Holder equal to the excess of (i) the
value of the Substitute Option without giving effect to the limitation in the
first sentence of this subsection (f) over (ii) the value of the Substitute
Option after giving effect to the limitation in the first sentence of this
subsection (f). This difference in value shall be determined by a nationally-
recognized investment banking firm selected by Holder.

     (g) Issuer shall not enter into any transaction described in subsection (b)
of this Section 7 unless the Acquiring Corporation and any person that controls
the Acquiring Corporation assume in writing all the obligations of Issuer
hereunder and take all other actions that may be necessary so that the
provisions of this Section 7 are given full force and effect (including, without
limitation, any action that may be necessary so that the holders of the other
shares of common stock issued by Substitute Option Issuer are not entitled to
exercise any rights by reason of the issuance or exercise of the Substitute
Option and the shares of Substitute Common Stock are otherwise in no way
distinguishable from or have lesser economic value (other than any dimunition in
value resulting from the fact that the Substitute Common Stock are restricted
securities, as defined in Rule 144 under the Securities Act) than other shares
of common stock issued by Substitute Option Issuer).

     8.   REGISTRATION RIGHTS.

     (a) Demand Registration Rights.  Issuer shall, subject to the conditions
         --------------------------                                           
of subparagraph (c) below, if requested by any Holder or Owner, as applicable,
including Grantee and any permitted transferee ("Selling Shareholder"), as
expeditiously as possible prepare and file a registration statement under the
Securities Act if such registration is necessary in order to permit the sale or
other disposition of any or all shares of Issuer Common Stock or other
securities that have been acquired by or are issuable to the Selling Shareholder
upon exercise of the Option in accordance with the intended method of sale or
other disposition stated by the Selling Shareholder in such request, including
without limitation a "shelf" registration statement under Rule 415 under the
Securities Act or any successor provision, and Issuer shall use its best efforts
to qualify such shares or other securities for sale under any applicable state
securities laws.  Grantee shall have the right to demand no more than two
registrations pursuant to this paragraph.  If requested by Grantee in connection
with any such registration, Issuer and Grantee shall provide each other with
representatives, warranties, indemnities and other agreements customarily given
in connection with such registration. If requested by Grantee in connection with
any such registration, Issuer and Grantee shall become party to any underwriting
agreement relating to the sale of the Option Shares, but only to the extent of
obligating themselves in respect of representations, warranties, indemnities and
other agreement customarily included in such underwriting agreements.

                                      E-9
<PAGE>
 
     (b) Additional Registration Rights.  If Issuer at any time after the
         ------------------------------                                  
exercise of the Option proposes to register any shares of Issuer Common Stock
under the Securities Act in connection with an underwritten public offering of
such Issuer Common Stock, Issuer will promptly give written notice to the
Selling Shareholders of its intention to do so and, upon the written request of
any Selling Shareholder given within 30 days after receipt of any such notice
(which request shall specify the number of shares of Issuer Common Stock
intended to be included in such underwritten public offering by the Selling
Shareholder), Issuer will cause all such shares for which a Selling Shareholder
requests participation in such registration, to be so registered and included in
such underwritten public offering; PROVIDED, HOWEVER, that Issuer may elect to
not cause any such shares to be so registered (i) if the underwriters in good
faith object for valid business reasons, or (ii) in the case of a registration
solely to implement an employee benefit plan or a registration filed on Form S-
4; PROVIDED, FURTHER, HOWEVER, that such election pursuant to (i) may only be
made two times. If some but not all the shares of Issuer Common Stock, with
respect to which Issuer shall have received requests for registration pursuant
to this subsection (b) shall be excluded from such registration, Issuer shall
make appropriate allocation of shares to be registered among the Selling
Shareholders desiring to register their shares pro rata in the proportion that
the number of shares requested to be registered by each such Selling Shareholder
bears to the total number of shares requested to be registered by all such
Selling Shareholders then desiring to have Issuer Common Stock registered for
sale.

     (c) Conditions to Required Registration.  Issuer shall use all reasonable
         -----------------------------------                                  
efforts to cause each registration statement referred to in subparagraph (a)
above to become effective and to obtain all consents or waivers of other parties
which are required therefor and to keep such registration statement effective,
PROVIDED, HOWEVER, that Issuer may delay any registration of Option Shares
required pursuant to subparagraph (a) above for a period not exceeding 180 days
provided Issuer shall in good faith determine that any such registration would
adversely affect an offering or contemplated offering of other securities by
Issuer, and Issuer shall not be required to register Option Shares under the
Securities Act pursuant to subsection (a) above:

          (i) prior to the earliest of (a) termination of the Plan pursuant to
     Section 6.1 thereof, (b) failure to obtain the requisite stockholder
     approval pursuant to Section 4.8 of the Plan, and (c) a Purchase Event or a
     Preliminary Purchase Event;

          (ii) on more than one occasion during any calendar year;

          (iii)  within 90 days after the effective date of a registration
     referred to in subsection (b) above pursuant to which the Selling
     Shareholder or Selling Shareholders concerned were afforded the opportunity
     to register such shares under the Securities Act and such shares were
     registered as requested; and

          (iv) unless a request therefor is made to Issuer by Selling
     Shareholders that hold at least 25% or more of the aggregate number of
     Option Shares (including shares of Issuer Common Stock issuable upon
     exercise of the Option) then outstanding.

                                      E-10
<PAGE>
 
     In addition to the foregoing, Issuer shall not be required to maintain the
effectiveness of any registration statement after the expiration of nine months
from the effective date of such registration statement. Issuer shall use all
reasonable efforts to make any filings, and take all steps, under all applicable
state securities laws to the extent necessary to permit the sale or other
disposition of the Option Shares so registered in accordance with the intended
method of distribution for such shares, PROVIDED, HOWEVER, that Issuer shall not
be required to consent to general jurisdiction or qualify to do business in any
state where it is not otherwise required to so consent to such jurisdiction or
to so qualify to do business.

     (d) Expenses.  Except where applicable state law prohibits such payments,
         --------                                                             
Issuer will pay all expenses (including without limitation registration fees,
qualification fees, blue sky fees and expenses (including the fees and expenses
of counsel), legal expenses, including the reasonable fees and expenses of one
counsel to the holders whose Option Shares are being registered, printing
expenses and the costs of special audits or "cold comfort" letters, expenses of
underwriters, excluding discounts and commissions but including liability
insurance if Issuer so desires or the underwriters so require, and the
reasonable fees and expenses of any necessary special experts) in connection
with each registration pursuant to subsection (a) or (b) above (including the
related offerings and sales by holders of Option Shares) and all other
qualifications, notifications or exemptions pursuant to subsection (a) or (b)
above.

     (e) Indemnification.  In connection with any registration under Section
         ---------------                                                    
8(a) or 8(b) of this Agreement, Issuer hereby indemnifies the Selling
Shareholders, and each underwriter thereof, including each person, if any, who
controls such holder or underwriter within the meaning of Section 15 of the
Securities Act, against all expenses, losses, claims, damages and liabilities
caused by any untrue, or alleged untrue, statement of a material fact contained
in any registration statement or prospectus or notification or offering circular
(including any amendments or supplements thereto) or any preliminary prospectus,
or caused by any omission, or alleged omission, to state therein a material fact
required to be stated therein or necessary to make the statements therein not
misleading, except insofar as such expenses, losses, claims, damages or
liabilities of such indemnified party are caused by any untrue statement or
alleged untrue statement that was included by Issuer in any such registration
statement or prospectus or notification or offering circular (including any
amendments or supplements thereto) in reliance upon and in conformity with,
information furnished in writing to Issuer by such indemnified party expressly
for use therein, and Issuer and each officer, director and controlling person of
Issuer shall be indemnified by such Selling Shareholders, or by such
underwriter, as the case may be, for all such expenses, losses, claims, damages
and liabilities caused by any untrue, or alleged untrue, statement that was
included by issuer in any such registration statement or prospectus or
notification or offering circular (including any amendments or supplements
thereto) in reliance upon, and in conformity with, information furnished in
writing to Issuer by such holder or such underwriter, as the case may be,
expressly for such use.

     Promptly upon receipt by a party indemnified under this Section 8(e) of
notice of the commencement of any action against such indemnified party in
respect of which indemnity or 

                                      E-11
<PAGE>
 
reimbursement may be sought against any indemnifying party under this Section
8(e), such indemnified party shall notify the indemnifying party in writing of
the commencement of such action, but the failure so to notify the indemnifying
party shall not relieve it of any liability which it may otherwise have to any
indemnified party under this Section 8(e). In case notice of commencement of any
such action shall be given to the indemnifying party as above provided, the
indemnifying party shall be entitled to participate in and, to the extent it may
wish, jointly with any other indemnifying party similarly notified, to assume
the defense of such action at its own expense, with counsel chosen by it and
satisfactory to such indemnified party. The indemnified party shall have the
right to employ separate counsel in any such action and participate in the
defense thereof, but the fees and expenses of such counsel (other than
reasonable costs of investigation) shall be paid by the indemnified party unless
(i) the indemnifying party either agrees to pay the same, (ii) the indemnifying
party fails to assume the defense of such action with counsel satisfactory to
the indemnified party, or (iii) the indemnified party has been advised by
counsel that one or more legal defenses may be available to the indemnifying
party that may be contrary to the interest of the indemnified party, in which
case the indemnifying party shall be entitled to assume the defense of such
action notwithstanding its obligation to bear fees and expenses of such counsel.
No indemnifying party shall be liable for any settlement entered into without
its consent, which consent may not be unreasonably withheld.

     If the indemnification provided for in this Section 8(e) is unavailable to
a party otherwise entitled to be indemnified in respect of any expenses, losses,
claims, damages or liabilities referred to herein, then the indemnifying party,
in lieu of indemnifying such party otherwise entitled to be indemnified shall
contribute to the amount paid or payable by such party to be indemnified as a
result of such expenses, losses, claims, damages or liabilities in such
proportion as is appropriate to reflect the relative benefits received by
Issuer, the Selling Shareholders and the underwriters from the offering of the
securities and also the relative fault of Issuer, the Selling Shareholders, and
the underwriters in connection with the statements or omissions which resulted
in such expenses, losses, claims, damages or liabilities, as well as any other
relevant equitable considerations.  The amount paid or payable by a party as a
result of the expenses, losses, claims, damages and liabilities referred to
above shall be deemed to include any legal or other fees or expenses reasonably
incurred by such party in connection with investigating or defending any action
or claim; provided, however, that in no case shall any Selling Shareholder be
responsible, in the aggregate, for any amount in excess of the net offering
proceeds attributable to its Option Shares included in the offering.  No person
guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of
the Securities Act) shall be entitled to contribution from any person who was
not guilty of such fraudulent misrepresentation. Any obligation by any holder to
indemnify shall be several and not joint with other holders.

     In connection with any registration pursuant to Section 8(a) or 8(b) of
this Agreement, Issuer and each Selling Shareholder (other than Grantee) shall
enter into an agreement containing the indemnification provisions of Section
8(e) of this Agreement.

                                      E-12
<PAGE>
 
     (f) Miscellaneous Reporting.  Issuer shall comply with all reporting
         -----------------------                                         
requirements and will do all such other things as may be necessary to permit the
expeditious sale at any time of any Option Shares by the Selling Shareholders
thereof in accordance with and to the extent permitted by any rule or regulation
promulgated by the SEC from time to time, including, without limitation, Rule
144A. Issuer shall at its expense provide the Selling Shareholders with any
information necessary in connection with the completion and filing of any
reports or forms required to be filed by them under the Securities Act or the
Exchange Act, or required pursuant to any state securities laws or the rules of
any stock exchange.

     (g) Issuer Taxes.  Issuer will pay all stamp taxes in connection with the
         ------------                                                         
issuance and the sale of the Option Shares and in connection with the exercise
of the Option, and will save the Selling Shareholders harmless, without
limitation as to time, against any and all liabilities, with respect to all such
taxes.

     9.   QUOTATION; LISTING.  If Issuer Common Stock or any other securities to
be acquired in connection with the exercise of the Option are then authorized
for quotation or trading or listing on the Nasdaq National Market or any
securities exchange, Issuer, upon the request of Holder, will promptly file an
application, if required, to authorize for quotation or trading or listing the
shares of Issuer Common Stock or other securities to be acquired upon exercise
of the Option on the Nasdaq National Market or such other securities exchange
and will use its best efforts to obtain approval, if required, of such quotation
or listing as soon as practicable.

     10.  DIVISION OF OPTION.  This Agreement (and the Option granted hereby)
are exchangeable, without expense, at the option of Holder, upon presentation
and surrender of this Agreement at the principal office of Issuer for other
Agreements providing for Options of different denominations entitling the holder
thereof to purchase in the aggregate the same number of shares of Issuer Common
Stock purchasable hereunder. The terms "Agreement" and "Option" as used herein
include any other Agreements and related Options for which this Agreement (and
the Option granted hereby) may be exchanged. Upon receipt by Issuer of evidence
reasonably satisfactory to it of the loss, theft, destruction or mutilation of
this Agreement, and (in the case of loss, theft or destruction) of reasonably
satisfactory indemnification, and upon surrender and cancellation of this
Agreement, if mutilated, Issuer will execute and deliver a new Agreement of like
tenor and date. Any such new Agreement executed and delivered shall constitute
an additional contractual obligation on the part of Issuer, whether or not the
Agreement so lost, stolen, destroyed or mutilated shall at any time be
enforceable by anyone.

     11.  MISCELLANEOUS.

     (a) Expenses.  Each of the parties hereto shall bear and pay all costs and
         --------                                                              
expenses incurred by it or on its behalf in connection with the transactions
contemplated hereunder, including fees and expenses of its own financial
consultants, investment bankers, accountants and counsel.

                                      E-13
<PAGE>
 
     (b) Waiver and Amendment.  Any provision of this Agreement may be waived at
         --------------------                                                   
any time by the party that is entitled to the benefits of such provision. This
Agreement may not be modified, amended, altered or supplemented except upon the
execution and delivery of a written agreement executed by the parties hereto.

     (c) Entire Agreement: no Third-party Beneficiary; Severability.  This
         ----------------------------------------------------------       
Agreement, together with the Plan and the other documents and instruments
referred to herein and therein, between Grantee and Issuer (a) constitutes the
entire agreement and supersedes all prior agreements and understandings, both
written and oral, between the parties with respect to the subject matter hereof
and (b) is not intended to confer upon any person other than the parties hereto
(other than any transferees of the Option Shares or any permitted transferee of
this Agreement pursuant to subsection (h) of this Section 11 and other than
indemnified parties under subsection (e) of Section 8) any rights or remedies
hereunder. If any term, provision, covenant or restriction of this Agreement is
held by a court of competent jurisdiction or a federal or state regulatory
agency to be invalid, void or unenforceable, the remainder of the terms,
provisions, covenants and restrictions of this Agreement shall remain in full
force and effect and shall in no way be affected, impaired or invalidated. If
for any reason such court or regulatory agency determines that the Option does
not permit Holder or Owner to acquire, or does not require Issuer to repurchase,
the full number of shares of Issuer Common Stock as provided in Section 3 (as
adjusted pursuant to Section 7), it is the express intention of Issuer to allow
Holder or Owner to acquire or to require Issuer to repurchase such lesser number
of shares as may be permissible without any amendment or modification hereof.

     (d) Governing Law.  This Agreement shall be governed and construed in
         -------------                                                    
accordance with the laws of the State of Delaware without regard to any
applicable conflicts of law rules.

     (e) Descriptive Headings.  The descriptive headings contained herein are
         --------------------                                                
for convenience of reference only and shall not affect in any way the meaning or
interpretation of this Agreement.

     (f) Notices.  All notices and other communications hereunder shall be in
         -------                                                             
writing and shall be deemed given if delivered personally, telecopied (with
confirmation) or mailed by registered or certified mail (return receipt
requested) to the parties at the following addresses (or at such other address
for a party as shall be specified by like notice):

     If to Issuer, to:   Bayonne Bancshares, Inc.
                         586 Broadway
                         Bayonne, New Jersey 07002
                         Facsimile: (201) 437-2912
                         Attention: Patrick F.X. Nilan
                                    Chairman of the Board

                                      E-14
<PAGE>
 
     With copies to:     Bayonne Bancshares, Inc.
                         586 Broadway
                         Bayonne, New Jersey 07002
                         Facsimile: (201) 437-5958
                         Attention: Thomas M. Coughlin
                                    Corporate Secretary

          and            Paul M. Aguggia, Esq.
                         Breyer & Aguggia LLP
                         1300 I Street, N.W., Suite 470 East
                         Washington, DC  20005
                         Facsimile: (201) (737-7979)

     If to Grantee, to:  Richmond County Financial Corp.
                         1214 Castleton Avenue
                         Staten Island, New York  10310
                         Facsimile: (718) 390-0224
                         Attention: Michael F. Manzulli
                                    Chairman of the Board and
                                     Chief Executive Officer

     With copies to:     Richmond County Financial Corp.
                         1214 Castleton Avenue
                         Staten Island, New York  10310
                         Facsimile: (718) 390-0224
                         Attention: Thomas R. Cangemi
                                    Senior Vice President, Chief Financial
                                     Officer and Secretary

          and            Douglas P. Faucette, Esq.
                         Muldoon, Murphy & Faucette
                         5101 Wisconsin Avenue, N.W.
                         Washington, D.C.  20016
                         Facsimile: (202) 966-9409
                       
     (g) Counterparts.  This Agreement and any amendments hereto may be executed
         ------------                                                           
in two counterparts, each of which shall be considered one and the same
agreement and shall become effective when both counterparts have been signed, it
being understood that both parties need not sign the same counterpart.

     (h) Assignment.  Neither this Agreement nor any of the rights, interests or
         ----------                                                             
obligations hereunder or under the Option shall be assigned by any of the
parties hereto (whether by operation of law or otherwise) without the prior
written consent of the other party, except that Holder may 

                                      E-15
<PAGE>
 
assign this Agreement to a wholly-owned subsidiary of Holder and Holder may
assign its rights hereunder in whole or in part after the occurrence of a
Purchase Event. Subject to the preceding sentence, this Agreement shall be
binding upon, inure to the benefit of and be enforceable by the parties and
their respective successors and assigns.

     (i) Further Assurances.  In the event of any exercise of the Option by the
         ------------------                                                    
Holder, Issuer and the Holder shall execute and deliver all other documents and
instruments and take all other action that may be reasonably necessary in order
to consummate the transactions provided for by such exercise.

     (j) Specific Performance.  The parties hereto agree that this Agreement may
         --------------------                                                   
be enforced by either party through specific performance, injunctive relief and
other equitable relief. Both parties further agree to waive any requirement for
the securing or posting of any bond in connection with the obtaining of any such
equitable relief and that this provision is without prejudice to any other
rights that the parties hereto may have for any failure to perform this
Agreement.

     IN WITNESS WHEREOF, Issuer and Grantee have caused this Stock Option
Agreement to be signed by their respective officers thereunto duly authorized,
all as of the day and year first written above.

                            BAYONNE BANCSHARES, INC.


                            By: /s/   Patrick F.X. Nilan
                                -----------------------------------------------
                            NAME:  Patrick F.X. Nilan
                            TITLE: Chairman of the Board


                            RICHMOND COUNTY FINANCIAL CORP.


                            By: /s/  Michael F. Manzulli
                                -----------------------------------------------
                            NAME:  Michael F. Manzulli
                            TITLE: Chairman of the Board and
                                   Chief Executive Officer
 

                                      E-16


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