DIME BANCORP INC
SC TO-I, EX-99.A.1.A, 2000-08-01
SAVINGS INSTITUTION, FEDERALLY CHARTERED
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<PAGE>   1
                                                              Exhibit (a)(1)(A)

                                  [DIME LOGO]
                               DIME BANCORP, INC.

                           OFFER TO PURCHASE FOR CASH
                  SHARES OF COMMON STOCK OF DIME BANCORP, INC.
           (INCLUDING THE ASSOCIATED PREFERRED STOCK PURCHASE RIGHTS)

OUR OFFER AND YOUR RIGHT TO WITHDRAW YOUR SHARES WILL EXPIRE AT 12:00 MIDNIGHT,
NEW YORK CITY TIME, ON MONDAY, AUGUST 28, 2000, UNLESS THE OFFER IS EXTENDED. WE
MAY EXTEND THE OFFER PERIOD AT ANY TIME.

DIME BANCORP, INC. IS:

- offering to purchase 13,607,664 shares of our common stock in a tender offer,
  and

- offering to purchase these shares at a price not greater than $18.00 nor less
  than $16.00 per share in cash, without interest.

IF YOU WANT TO TENDER YOUR SHARES INTO OUR OFFER, YOU SHOULD:

- specify the price between $16.00 and $18.00 at which you are willing to tender
  your shares,

- specify the amount of shares you want to tender, and

- follow the instructions in this document and the related documents, including
  the accompanying letter of transmittal, to submit your shares.

WHEN OUR OFFER EXPIRES:

- we will select the lowest purchase price specified by tendering stockholders
  that will allow us to purchase 13,607,664 shares or such lesser number of
  shares as are tendered,

- if the number of shares tendered at or below the selected price is not more
  than 13,607,664, we will purchase all these shares at that price, and

- if the number of shares tendered at or below the selected price is more than
  13,607,664, we will purchase shares at the selected price

  - first from holders of less than 100 shares who tendered all of their shares
    at or below the selected price, and

  - then, on a pro rata basis, from all other stockholders who tendered shares
    at or below the selected price.

Our offer is not conditioned on any minimum number of shares being tendered. Our
offer is, however, subject to other conditions discussed in Section 7.

Our Board of Directors has approved this offer. However, neither we nor our
Board of Directors nor the information agent nor either of the dealer managers
makes any recommendation to you as to whether you should tender or not tender
your shares or as to the price or prices at which you may choose to tender your
shares. You must make your own decision as to whether to tender your shares and,
if so, how many shares to tender and the price or prices at which your shares
should be tendered.

This document contains important information about our offer. We urge you to
read it in its entirety.

                     The dealer managers for our offer are:

CREDIT SUISSE FIRST BOSTON                                   MERRILL LYNCH & CO.

August 1, 2000
<PAGE>   2

                              IMPORTANT PROCEDURES

If you want to tender all or part of your shares, you must do one of the
following before our offer expires:

     - if your shares are registered in the name of a broker, dealer, commercial
       bank, trust company or other nominee, contact the nominee and have the
       nominee tender your shares for you,

     - if you hold certificates in your own name, complete and sign a letter of
       transmittal according to its instructions, and deliver it, together with
       any required signature guarantee, the certificates for your shares and
       any other documents required by the letter of transmittal, to EquiServe
       Trust Company, N.A., the depositary for our offer,

     - if you want to tender shares held in either the Retirement 401(k)
       Investment Plan of Dime or the North American Mortgage Company Retirement
       and 401(k) Savings Plan, follow the separate instructions and procedures
       described in either the "Letter to Participants in the Retirement 401(k)
       Investment Plan of Dime Bancorp, Inc." or the "Letter to Participants in
       the North American Mortgage Company Retirement and 401(k) Savings Plan,"
       as applicable and as described in Section 3 of this document,

     - if you want to tender shares held in the Dime Bancorp, Inc. Dividend
       Reinvestment and Optional Cash Purchase Program, you should follow the
       instructions and complete the boxes set forth in the letter of
       transmittal to instruct the program administrator to tender your shares,
       or

     - if you are an institution participating in The Depository Trust Company,
       which we call the "book-entry transfer facility" in this document, tender
       your shares according to the procedure for book-entry transfer described
       in Section 3.

If you want to tender your shares but

     - your certificates for the shares are not immediately available or cannot
       be delivered to the depositary, or

     - you cannot comply with the procedure for book-entry transfer, or

     - your other required documents cannot be delivered to the depositary by
       the expiration of our offer,

you can still tender your shares if you comply with the guaranteed delivery
procedure described in Section 3.

     TO TENDER YOUR SHARES YOU MUST FOLLOW THE PROCEDURES DESCRIBED IN THIS
DOCUMENT, THE LETTER OF TRANSMITTAL AND THE OTHER DOCUMENTS RELATED TO OUR
OFFER, INCLUDING CHOOSING A PRICE AT WHICH YOU WANT TO TENDER YOUR SHARES.

     If you wish to maximize the chance that your shares will be purchased by
us, you should check the box next to "Shares tendered at price determined
pursuant to the offer" in the section of the letter of transmittal called "Price
At Which You Are Tendering." Note that this election could result in your shares
being purchased at the minimum price of $16.00 per share.

     If you have any questions or need assistance, you should contact Innisfree
M&A Incorporated, which is the information agent for our offer, or Credit Suisse
First Boston Corporation ("Credit Suisse First Boston") or Merrill Lynch,
Pierce, Fenner & Smith Incorporated ("Merrill Lynch"), which are the dealer
managers for our offer, at their addresses and telephone numbers on the back
page of this document. You may request additional copies of this document, the
letter of transmittal or the notice of guaranteed delivery from the information
agent.

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                               TABLE OF CONTENTS

<TABLE>
<CAPTION>
SECTION                                                       PAGE
-------                                                       ----
<S>                                                           <C>
Summary.....................................................    1
Forward-Looking Statements..................................    6
Dime's Tender Offer.........................................    7
  Section 1.   Number of Shares; Price; Priority of
               Purchase.....................................    7
  Section 2.   Recent Developments; Purposes of Our Offer...    9
  Section 3.   Procedures for Tendering Shares..............   19
  Section 4.   Withdrawal Rights............................   25
  Section 5.   Purchase of Shares and Payment of Purchase
               Price........................................   26
  Section 6.   Conditional Tender Procedures................   27
  Section 7.   Conditions of Our Offer......................   28
  Section 8.   Price Range of Shares; Dividends; Our Rights
               Agreement....................................   29
  Section 9.   Source and Amount of Funds...................   31
  Section 10.  Information About Us.........................   31
  Section 11.  Information about Our Shares; Interest of
               Directors and Executive Officers;
               Transactions and Arrangements Concerning
               Shares.......................................   33
  Section 12.  Effects of Our Offer on the Market for
               Shares; Registration under the Exchange
               Act..........................................   35
  Section 13.  Legal Matters; Regulatory Approvals..........   35
  Section 14.  United States Federal Income Tax
               Consequences.................................   36
  Section 15.  Extension of Our Offer; Termination;
               Amendment....................................   38
  Section 16.  Fees and Expenses............................   39
  Section 17.  Miscellaneous................................   40
</TABLE>

                                       iii
<PAGE>   4

                                    SUMMARY

     We are providing this summary for your convenience. It highlights material
information in this document, but you should realize that it does not describe
all of the details of our offer to the same extent that they are described in
the body of this document. We urge you to read the entire document and the
related letter of transmittal because they contain the full details of our
offer. Where helpful, we have included references to the sections of this
document where you will find a more complete discussion.

WHO IS OFFERING TO PURCHASE MY
SHARES?                          Dime Bancorp, Inc. We are offering to purchase
                                 up to 13,607,664 shares of our outstanding
                                 common stock and the associated preferred stock
                                 purchase rights. See Section 10.

WHAT IS THE PURCHASE PRICE?      The price range for our offer is $16.00 to
                                 $18.00.

                                 We are conducting the offer through a procedure
                                 commonly called a "modified Dutch Auction."
                                 This procedure allows you to choose a price
                                 within this price range at which you are
                                 willing to sell your shares.

                                 We will look at the prices chosen by
                                 stockholders for all of the shares properly
                                 tendered. We will then select the lowest price
                                 that will allow us to buy 13,607,664 shares. If
                                 a lesser number of shares is tendered, we will
                                 select the price that will allow us to buy all
                                 shares that were properly tendered. All shares
                                 we purchase will be purchased at the same
                                 price, even if you have chosen a lower price,
                                 but we will not purchase any shares tendered at
                                 a price above the price selected in accordance
                                 with these procedures. No separate
                                 consideration will be paid for the associated
                                 preferred stock purchase rights.

                                 If you wish to maximize the chance that your
                                 shares will be purchased, you should check the
                                 box next to "Shares tendered at price
                                 determined pursuant to the offer" in the
                                 section of the letter of transmittal called
                                 "Price At Which You Are Tendering." You should
                                 understand that this election could result in
                                 your shares being purchased at the minimum
                                 price of $16.00 per share. See Section 1.

WHAT ARE THE "ASSOCIATED
PREFERRED
STOCK PURCHASE RIGHTS"?          The associated preferred stock purchase rights
                                 were issued to all stockholders but are not
                                 represented by a separate document. Instead,
                                 they are represented by the certificates for
                                 your shares. Unless the context otherwise
                                 requires, all references to shares include the
                                 associated preferred stock purchase rights,
                                 and, unless these rights are redeemed prior to
                                 the expiration of our offer, a tender of shares
                                 will include a tender of the associated rights.
                                 See Section 8 for a description of the rights
                                 and the agreement under which the rights were
                                 issued.

HOW AND WHEN WILL I BE PAID?     If your shares are purchased in our offer, you
                                 will be paid the purchase price, in cash,
                                 without interest, as soon as practicable after
                                 the expiration of the offer period and the
                                 acceptance of the shares for payment. There may
                                 be tax consequences to receiving this payment.
                                 See Sections 1, 3, 5 and 14.

HOW MANY SHARES WILL DIME
PURCHASE IN ALL?                 We will purchase up to 13,607,664 shares in our
                                 offer, or approximately 12.45% of our
                                 outstanding common stock before the investment
                                 by Warburg discussed in this document. We also

                                        1
<PAGE>   5

                                 reserve the right to purchase additional shares
                                 up to 2% of the outstanding shares, subject to
                                 applicable legal requirements. Our offer is not
                                 conditioned on any minimum number of shares
                                 being tendered. See Section 1.

IF I TENDER MY SHARES, HOW
MANY OF MY SHARES WILL DIME
PURCHASE?                        All the shares that you tender in our offer may
                                 not be purchased even if they are tendered at
                                 or below the purchase price we select. If more
                                 than 13,607,664 shares are tendered at or below
                                 the selected purchase price, we will purchase
                                 shares based on the following order of
                                 priority:

                                 - First, we will purchase shares from all
                                   holders of "odd lots" of less than 100 shares
                                   (including any shares held in our dividend
                                   reinvestment program, but not including any
                                   shares held in the Retirement 401(k)
                                   Investment Plan of Dime or the North American
                                   Mortgage Company Retirement and 401(k)
                                   Savings Plan) who properly tender all of
                                   their shares at prices equal to or below the
                                   selected price.

                                 - Second, we will purchase shares from all
                                   other stockholders who properly tender shares
                                   at prices equal to or below the selected
                                   price, on a pro rata basis, subject to the
                                   conditional tender provisions described in
                                   Section 6. As a result, we will purchase the
                                   same percentage of shares from each tendering
                                   stockholder in this second category. We will
                                   announce this proration percentage, if it is
                                   necessary, after our offer expires.

                                 As we noted above, we may also choose to
                                 purchase an additional 2% of the outstanding
                                 shares, subject to applicable legal rules. See
                                 Section 1.

HOW WILL DIME PAY FOR THE
SHARES?                          We would need a maximum of $244,937,952 to
                                 purchase 13,607,664 shares at $18.00. We
                                 recently announced that Warburg, Pincus Equity
                                 Partners, L.P. had agreed to invest
                                 approximately $238 million in cash in Dime. We
                                 will use this cash and other cash we have
                                 available to pay for the shares we purchase in
                                 this offer. See Sections 2 and 9.

HOW LONG DO I HAVE TO TENDER
MY SHARES TO DIME?               You may tender your shares until our offer
                                 expires. Right now, the offer is scheduled to
                                 expire on Monday, August 28, 2000, at 12:00
                                 midnight, New York City time, but we may choose
                                 to extend it at any time. We cannot assure you
                                 that we will extend our offer or, if we extend
                                 it, for how long it will be extended. See
                                 Sections 1 and 15.

HOW WILL I BE NOTIFIED IF DIME
EXTENDS THIS OFFER?              If our offer is extended, we will make a public
                                 announcement before 9:00 a.m., New York City
                                 time, on the first business day after the offer
                                 was scheduled to expire. See Section 15.

WHAT ARE THE CONDITIONS TO
DIME'S OFFER?                    Our obligation to accept and pay for your
                                 tendered shares is conditioned upon the
                                 satisfaction or waiver of the conditions to
                                 Warburg's investment. In addition, our offer is
                                 conditioned on North Fork not successfully
                                 completing its hostile offer and a number of
                                 general conditions that are described in this
                                 document. See Sections 2 and 7.

                                        2
<PAGE>   6

WHAT ARE THE TERMS OF
WARBURG'S INVESTMENT IN DIME?    For a total of $238 million, Warburg intends to
                                 purchase a variety of securities indirectly
                                 representing a total of about 13.6 million
                                 shares of our common stock and an equivalent
                                 number of 7-year warrants with an exercise
                                 price of $21.50 per underlying common share
                                 (subject to adjustments). On July 6, 2000,
                                 Warburg purchased a large portion of these
                                 securities for $210 million. Upon receipt of
                                 necessary regulatory actions, such as antitrust
                                 clearance under the Hart-Scott-Rodino Antitrust
                                 Improvements Act of 1976 and a determination by
                                 the Office of Thrift Supervision that Warburg
                                 does not control us, Warburg is expected to
                                 purchase the remaining securities under our
                                 agreement with them for about $28 million. See
                                 Section 2.

HOW DO I TENDER MY SHARES?       To tender your shares, you must complete one of
                                 the actions described under "Important
                                 Procedures" on the inside front cover of this
                                 document before our offer expires.

                                 You may also contact the information agent,
                                 either of the dealer managers or your broker
                                 for assistance. The contact information for the
                                 information agent and each of the dealer
                                 managers is on the back page of this document.

                                 See Section 3 and the instructions to the
                                 letter of transmittal.

ONCE I HAVE TENDERED SHARES IN
THE OFFER, CAN I CHANGE MY
MIND?                            Yes. If you tender your shares and change your
                                 mind, you may withdraw your shares at any time
                                 before our offer expires.

                                 In addition, after our offer expires, if we
                                 have not accepted for payment the shares you
                                 have tendered to us, you may withdraw your
                                 shares at any time after 12:00 midnight, New
                                 York City time, on Tuesday, September 26, 2000.
                                 See Section 4.

                                 To withdraw your shares, you must timely
                                 deliver a written notice of your withdrawal to
                                 the depositary at the address or facsimile
                                 number appearing on the back page of this
                                 document. Your notice of withdrawal must
                                 specify your name, the number of shares to be
                                 withdrawn and the name of the registered holder
                                 of the shares. Some additional requirements
                                 apply if the certificates for shares to be
                                 withdrawn have been delivered to the depositary
                                 or if your shares have been tendered under the
                                 procedure for book-entry transfer set forth in
                                 Section 3. See Section 4.

IF I DECIDE NOT TO TENDER ANY
OF MY SHARES TO DIME, HOW WILL
THE OFFER AFFECT MY SHARES?      We are in the process of issuing preferred
                                 stock to Warburg in connection with its
                                 investment in us. If both that investment and
                                 this offer are fully completed, the preferred
                                 stock issued to Warburg should offset the stock
                                 purchased in this offer. Accordingly, if you do
                                 not tender any of your shares, your percentage
                                 ownership interest in Dime after the offer
                                 should be about the same as your interest
                                 before Warburg's investment. We are also
                                 selling warrants to Warburg. If Warburg
                                 exercises these warrants and pays the exercise
                                 price, your percentage ownership interest in
                                 Dime will decrease. The exercise price for the
                                 warrants is currently $21.50 per underlying
                                 common share. See Section 2.

                                        3
<PAGE>   7

WHAT DO DIME AND ITS BOARD OF
DIRECTORS THINK ABOUT THIS
OFFER?                           Our board of directors has approved this offer.
                                 However, neither we nor our board of directors
                                 nor the information agent nor either of the
                                 dealer managers is making any recommendation
                                 regarding whether you should tender or not
                                 tender your shares or at what price you should
                                 choose to tender your shares. You must decide
                                 whether to tender your shares and, if so, how
                                 many shares to tender and the price or prices
                                 at which you will tender them. You should
                                 discuss whether to tender your shares with your
                                 broker or other financial or tax advisor. Our
                                 directors and executive officers have advised
                                 us that they do not intend to tender any of
                                 their shares in our offer. See Section 2.

WHAT IS A RECENT MARKET PRICE
OF MY DIME SHARES?               Our common stock is traded on the NYSE under
                                 the symbol "DME." On July 28, 2000, a date
                                 close to the date of this document, the closing
                                 price on the NYSE Composite Tape was $16 3/16.
                                 We urge you to obtain more current market
                                 quotations for your shares. See Section 8.

WILL I HAVE TO PAY BROKERAGE
COMMISSIONS OR STOCK TRANSFER
TAX IF I TENDER MY SHARES TO
DIME?                            If you are a registered stockholder and tender
                                 your shares directly to the depositary, you
                                 will not need to pay any brokerage commissions.
                                 If you hold shares through a broker or bank,
                                 however, you should ask your broker or bank to
                                 see if you will be charged a fee to tender your
                                 shares. See Section 3.

                                 If you instruct the depositary in the letter of
                                 transmittal to make the payment for the shares
                                 to the registered holder, you will not incur
                                 any stock transfer tax. See Section 5.

WHAT ARE THE UNITED STATES
FEDERAL INCOME TAX CONSEQUENCES
IF I TENDER MY SHARES TO DIME?   Generally, you will be subject to United States
                                 federal income taxation when you receive cash
                                 from us in exchange for the shares you tender.
                                 The cash you receive will be treated either as:

                                 - a sale or exchange eligible for capital gains
                                   treatment or

                                 - a dividend subject to ordinary income tax
                                   rates.

                                 See Section 14.

WHAT IF I ALREADY TENDERED MY
DIME SHARES TO NORTH FORK, BUT
NOW WANT TO TENDER THEM TO
DIME INSTEAD?                    If you have already tendered your shares to
                                 North Fork Bancorporation, Inc. in response to
                                 its hostile offer, you must properly withdraw
                                 them before you can tender them to us. To
                                 effectively withdraw, North Fork's exchange
                                 agent must receive a written notice from you
                                 before North Fork's offer expires either at one
                                 of the addresses listed below or by facsimile
                                 at (201) 324-3402 or (201) 324-3403 (you may
                                 confirm your facsimile by telephone at (201)
                                 222-4707). The written notice must contain your
                                 name, address, social security number, the
                                 number of shares you would like to withdraw,
                                 the certificate numbers of your shares and the
                                 name of the registered holder of your shares,
                                 if different from the person who tendered the
                                 shares. All signatures on the notice of
                                 withdrawal must be guaranteed by a financial
                                 institution in accordance with the procedures
                                 set forth in North Fork's prospectus under "The
                                 Offer-Withdrawal Rights." If your shares have
                                 been tendered in North Fork's hostile offer
                                 through book-entry tender procedures at The
                                 Depository Trust Company (or DTC), a notice of
                                 withdrawal must also specify the name and
                                 account number at The

                                        4
<PAGE>   8

                                 Depository Trust Company and otherwise comply
                                 with The Depository Trust Company's procedures.
                                 See Section 3.

                                 By Mail:

                                 First Chicago Trust Company of New York
                                 Attention: Corporate Actions
                                 Suite 4660
                                 P.O. Box 2569
                                 Jersey City, NJ 07303-2569

                                 By Hand:

                                 First Chicago Trust Company of New York
                                 Attention: Corporate Actions
                                 c/o Securities Transfer & Reporting Services
                                 Inc.
                                 100 William Street, Galleria
                                 New York, NY 10038

                                 By Overnight, Certified or Express Mail
                                 Delivery:

                                 First Chicago Trust Company of New York
                                 Attention: Corporate Actions
                                 525 Washington Blvd.
                                 Jersey City, NJ 07310

                                 If you have any questions regarding withdrawal
                                 of any of your shares that you already tendered
                                 to North Fork, our information agent, Innisfree
                                 M&A Incorporated, can assist you. Their contact
                                 information is on the back page of this
                                 document.

WHOM DO I CONTACT IF I HAVE
QUESTIONS ABOUT DIME'S OFFER?    Our information agent or dealer managers can
                                 help answer your questions. The information
                                 agent is Innisfree M&A Incorporated and the
                                 dealer managers are Credit Suisse First Boston
                                 and Merrill Lynch. Their contact information
                                 appears on the back page of this document.

                                        5
<PAGE>   9

                           FORWARD-LOOKING STATEMENTS

     This document contains a number of forward-looking statements regarding the
financial condition, results of operations and business of Dime and other
companies. These statements may be made directly in this document or may be
incorporated in this document by reference to other documents. These statements
may also include references to periods following the completion of our offer or
other transactions described in this document. You can find many of these
statements by looking for words such as "believes," "expects," "anticipates,"
"estimates," "intends," "plans," "may," "will" and "potential" and for similar
expressions. Forward-looking statements involve substantial risks and
uncertainties. Some of the factors that may cause actual results to differ
materially from those contemplated by the forward-looking statements include,
but are not limited to, the following possibilities:

     - the timing and occurrence or non-occurrence of events, including the
       conditions to our offer, may be subject to circumstances beyond our
       control,

     - there may be increases in competitive pressure among financial
       institutions or from non-financial institutions,

     - changes in the interest rate environment may reduce interest margins or
       may adversely affect mortgage banking operations,

     - changes in deposit flows, loan demand or real estate values may adversely
       affect our business,

     - changes in accounting principles, policies or guidelines may cause our
       financial condition to be perceived differently,

     - general economic conditions, either nationally or in some or all of the
       states in which we do business, or conditions in securities markets, the
       banking industry or the mortgage banking industry, may be less favorable
       than we currently anticipate,

     - legislation or regulatory changes may adversely affect our business,

     - technological changes may be more difficult or expensive than we
       anticipate,

     - success or consummation of new business initiatives may be more difficult
       or expensive than we anticipate,

     - litigation or other matters before regulatory agencies, including
       litigation or matters related to North Fork's hostile offer and takeover
       attempt, whether currently existing or commencing in the future, may
       delay the occurrence or non-occurrence of events longer than we
       anticipate,

     - our current defense against North Fork's hostile offer and takeover
       attempt may be more costly than we anticipate, and

     - proactive or reactive actions taken by us in response to, or in
       connection with, North Fork's hostile offer and takeover attempt may
       occur at unforeseen times and may cause modification or termination of
       other planned actions.

     All subsequent written and oral forward-looking statements concerning our
offer or other matters addressed in this document and attributable to us or any
person acting on our behalf are qualified by these cautionary statements. We do
not undertake any obligation to release publicly any revisions to such
forward-looking statements to reflect events or circumstances after the date of
this document or to reflect the occurrence of unanticipated events.

                                        6
<PAGE>   10

                              DIME'S TENDER OFFER

SECTION 1.  NUMBER OF SHARES; PRICE; PRIORITY OF PURCHASE.

     GENERAL.  On the terms and subject to the conditions of our offer, we will
purchase 13,607,664 shares of our common stock, including the associated
preferred stock purchase rights, or such lesser number of shares as are properly
tendered and not properly withdrawn in accordance with Section 4, at a price not
greater than $18.00 nor less than $16.00 per share, net to the seller in cash,
without interest.

     The term "expiration date" with respect to our offer means 12:00 midnight,
New York City time, on Monday, August 28, 2000, unless we, in our sole
discretion, extend the period of time during which our offer will remain open.
If extended by us, the term "expiration date" will mean the latest time and date
at which our offer, as extended, will expire. See Section 15 for a description
of our right to extend, delay, terminate or amend our offer.

     In accordance with Instruction 5 of the letter of transmittal, stockholders
desiring to tender shares must specify the price or prices, not greater than
$18.00 nor less than $16.00 per share, at which they are willing to sell their
shares. Prices may be specified in increments of $0.125. Alternatively,
stockholders desiring to tender shares can choose not to specify a price and,
instead, specify that they will sell their shares at the purchase price selected
by us for shares properly tendered in our offer. This could result in the
tendering stockholder receiving a price per share as low as $16.00.

     As soon as practicable following the expiration date, we will select the
purchase price for shares properly tendered and not properly withdrawn, taking
into account the number of shares tendered and the prices specified by tendering
stockholders. We will select the lowest purchase price between $18.00 and $16.00
net per share in cash, without interest, that will enable us to purchase
13,607,664 shares, or such lesser number of shares as are properly tendered.

     Shares properly tendered at or below that purchase price and not properly
withdrawn will be purchased at the selected purchase price upon the terms and
conditions of our offer, including the odd lot, proration and conditional tender
provisions described below. If more than 13,607,664 shares are tendered at or
below the purchase price we select, shares tendered at or below the purchase
price will be subject to proration, except for odd lots. In accordance with the
rules of the Securities and Exchange Commission, we may, and we reserve the
right to, purchase in our offer an additional amount of shares, not to exceed 2%
of our outstanding common stock, without amending or extending our offer. See
Section 15.

     All shares we purchase will be purchased at the same price, even if you
have specified a lower price. However, we will not purchase any shares tendered
at a price above the purchase price we select using the procedures described
above.

     All shares tendered and not purchased, including shares tendered at prices
above the purchase price we select and shares not purchased because of proration
or the conditional tender procedures, will be returned to you at our expense as
soon as practicable following the expiration date.

     On the letter of transmittal you can specify the order in which portions of
your shares will be purchased if, as a result of the proration provisions or
otherwise, some but not all of your tendered shares are purchased in our offer.
In addition, you can tender different portions of your shares at different
prices by completing separate letters of transmittal for each price at which you
tender shares.

     You may withdraw your shares from our offer by following the procedures in
Section 4.

     If we:

     - increase or decrease the range of prices to be paid for shares,

     - increase the number of shares being sought in our offer by more than 2%
       of our outstanding common stock,

     - decrease the number of shares being sought in our offer, or

     - materially change the fees to be paid to our dealer managers,

                                        7
<PAGE>   11

then our offer must remain open, or will be extended, until at least ten
business days from, and including, the date that notice of any such change is
first published, sent or given in the manner described in Section 15. For
purposes of our offer, a "business day" means any day other than a Saturday,
Sunday or United States federal holiday and consists of the time period from
12:01 a.m. through 12:00 midnight, New York City time.

     In calculating the number of shares to be accepted for payment pursuant to
the procedures described in this document, we will add to the total number of
shares tendered at the minimum price of $16.00 the shares tendered by
stockholders who have indicated, in the appropriate box in the letter of
transmittal, that they are willing to accept the price determined in our offer.
Accordingly, shares tendered at the price determined in the offer will be
treated the same as shares tendered at $16.00. However, as discussed above,
shares properly tendered and accepted for purchase will all be purchased at the
same price, even if the purchase price we select is higher than the price at
which the shares were tendered.

     Unless the context otherwise requires, all references to shares in this
document and the documents related to our offer include the associated preferred
stock purchase rights, and, unless the rights are redeemed prior to the
expiration date of our offer, a tender of shares will also be a tender of the
associated preferred stock purchase rights. See Section 8 for a description of
the rights and the agreement under which the rights were issued.

     OUR OFFER IS NOT CONDITIONED ON ANY MINIMUM NUMBER OF SHARES BEING
TENDERED. OUR OFFER IS, HOWEVER, SUBJECT TO OTHER CONDITIONS. SEE SECTION 7.

     PRIORITY OF PURCHASES.  Upon the terms and conditions of our offer, if
13,607,664 or fewer shares are properly tendered at prices equal to or below the
purchase price and not properly withdrawn, we will purchase all properly
tendered shares at the purchase price.

     Upon the terms and conditions of our offer, if more than 13,607,664 shares
are properly tendered at prices equal to or below the purchase price and not
properly withdrawn, we will purchase properly tendered shares in the following
order:

     - First, all shares properly tendered and not properly withdrawn by any
       "odd lot holder" (as defined below) who:

        - tenders all shares owned (beneficially or of record) by the odd lot
          holder at a price equal to or below the purchase price (tenders of
          less than all the shares owned will not qualify for this preference);
          and

        - completes the section entitled "Odd Lots" in the letter of transmittal
          and, if applicable, in the notice of guaranteed delivery; and

     - Second, after the purchase of all the shares properly tendered by odd lot
       holders and subject to the conditional tender procedures described in
       Section 6, all other shares properly tendered at prices equal to or below
       the purchase price, on a pro rata basis with appropriate adjustments to
       avoid purchases of fractional shares, as described below.

As a result, all the shares that you tender in our offer may not be purchased,
even if they are tendered at prices equal to or below the purchase price. This
will occur if we receive more than 13,607,664 properly tendered shares at prices
equal to or below the purchase price.

     As we noted above, we may elect to purchase more than 13,607,664 shares in
our offer, subject to applicable law. If we do so, the preceding provisions will
apply to the greater number of shares.

     ODD LOTS.  For purposes of our offer, the term "odd lots" means all shares
properly tendered before the expiration date at prices equal to or below the
purchase price and not properly withdrawn by any person, referred to as an "odd
lot holder," who owns, beneficially or of record, a total of fewer than 100
shares (including any shares held in our dividend reinvestment program, but not
including any shares held in the Retirement 401(k) Investment Plan of Dime or
the North American Mortgage Company Retirement and 401(k) Savings Plan) and
certifies to that fact in the "Odd Lots" box on the letter of

                                        8
<PAGE>   12

transmittal and, if applicable, on the notice of guaranteed delivery. As set
forth above, odd lots will be accepted for payment before proration, if any, of
the purchase of other tendered shares. To qualify for this preference, an odd
lot holder must tender all shares owned, beneficially or of record, by the odd
lot holder in accordance with the procedures described in Section 3.

     This preference is not available to partial tenders or to beneficial or
record holders of a total of 100 or more shares, even if these holders have
separate accounts or certificates representing fewer than 100 shares. This
preference is also not available to any shares held in the Retirement 401(k)
Investment Plan of Dime or the North American Mortgage Company Retirement and
401(k) Savings Plan.

     Any odd lot holder wishing to tender all its shares pursuant to our offer
should complete the section entitled "Odd Lots" in the letter of transmittal
and, if applicable, in the notice of guaranteed delivery.

     We also reserve the right, but will not be obligated, to purchase all
shares properly tendered by any stockholder who tenders all shares owned
beneficially or of record at or below the purchase price and who, as a result of
proration, would then own a total of fewer than 100 shares. If we exercise this
right, it will increase the number of shares that we are offering to purchase in
our offer by the number of shares purchased through the exercise of this right,
subject to applicable law.

     PRORATION.  If proration of tendered shares is required, we will determine
the proration percentage as soon as practicable following the expiration date.
Subject to the conditional tender procedures described in Section 6, proration
for each stockholder tendering shares, other than odd lot holders, will be based
on the ratio of the number of shares properly tendered and not properly
withdrawn by the stockholder to the total number of shares properly tendered and
not properly withdrawn by all stockholders other than odd lot holders at or
below the purchase price selected by us.

     Because of the potential difficulty in determining the number of shares
properly tendered and not properly withdrawn, including shares tendered by
guaranteed delivery procedures as described in Section 3, and because of the odd
lot procedures described above and the conditional tender procedures described
in Section 6, we do not expect that we will be able to announce the final
proration percentage or commence payment for any shares purchased under our
offer until seven to ten business days after the expiration date. The
preliminary results of any proration will be announced by press release as soon
as practicable after the expiration date. Stockholders may obtain preliminary
proration information from the information agent or the dealer managers and may
be able to obtain this information from their brokers.

     As described in Section 14, the number of shares that we will purchase from
a stockholder under our offer may affect the United States federal income tax
consequences to that stockholder and, therefore, may be relevant to a
stockholder's decision whether or not to tender shares. The letter of
transmittal affords each stockholder the opportunity to designate the order of
priority in which shares are to be purchased in the event of proration, should a
stockholder decide to do so for federal income tax reasons. In addition,
stockholders may choose to submit a "conditional tender" under the procedures
discussed in Section 6 in order to structure their tender for federal income tax
reasons.

SECTION 2.  RECENT DEVELOPMENTS; PURPOSES OF OUR OFFER.

     DEVELOPMENTS.  On April 28, 2000, we announced that we would begin a
comprehensive exploration of all strategic options, in light of the termination
of our merger agreement with Hudson United Bancorp. This review of strategic
alternatives was undertaken with the goal of realizing the full value of our
franchise for the benefit of our stockholders, customers, employees and the
communities we serve.

     We believe that we undertook a comprehensive review of all currently
available strategic options through the following actions:

     - we undertook a detailed review of our business plan,

     - we engaged in discussions with two highly qualified potential merger
       partners with which we signed confidentiality agreements and exchanged
       information,

                                        9
<PAGE>   13

     - we reviewed our options with regard to financial partners and engaged in
       discussions with a financial investor (Warburg) with which we signed a
       confidentiality agreement and exchanged information, and

     - we continued to review and consider North Fork's proposal in light of the
       other strategic options we considered.

     We learned from the two potential merger partners that they had concluded,
primarily as a consequence of factors relating to them, the time was not right
for them to pursue an acquisition of Dime. In addition, as we and our financial
advisors analyzed the current market for bank combinations, it became clear to
us that the merger and acquisition market for depository institutions is at the
lowest point of activity in close to a decade and we believed that a sale of the
company at this moment in time would not optimize stockholder value. Therefore,
on July 6, 2000 we announced that, as a product of this comprehensive review, we
had developed the following initiatives approved by our board of directors with
the intention of helping to improve returns and provide enhanced value to our
stockholders:

     - This "modified Dutch auction" tender offer for a portion of the shares of
       our common stock,

     - A capital investment in Dime of $238 million by Warburg, Pincus Equity
       Partners, L.P.,

     - The appointment of Anthony P. Terracciano, an experienced and
       well-respected banking professional, as Chairman of our board of
       directors,

     - The adoption of amendments to our stockholder rights plan, and

     - The anticipated distribution of securities, known as litigation tracking
       warrants, to all of our stockholders (excluding Warburg) representing an
       interest in our pending "goodwill" lawsuit against the United States
       government.

     These initiatives may or may not be successful in increasing stockholder
value. See our discussion of "Forward Looking Statements."

     Each of these initiatives is discussed at greater length below. In
addition, we also discuss the current status of North Fork's hostile offer for
our common stock that was first announced on March 5, 2000.

     INVESTMENT BY WARBURG.  This section discusses the material terms of the
Investment Agreement between Dime and Warburg, dated July 6, 2000, and the
securities issued, or to be issued, by us to Warburg in exchange for Warburg's
$238 million investment in us. This information is not complete and is qualified
by reference to the Investment Agreement and its exhibits, which were filed with
the SEC on a Form 8-K, dated July 11, 2000. The Investment Agreement and its
exhibits are incorporated into this document by reference.

     Warburg's investment is being made over two closings. The first closing
occurred upon signing the Investment Agreement on July 6. The second closing
will occur following receipt of necessary regulatory approvals. The transactions
are described below.

          First Closing.  On July 6, 2000, Warburg purchased rights to
     12,009.491 shares of Series B junior voting preferred stock, representing
     about 9.9% of Dime's outstanding common stock after issuance of the Series
     B stock, as each share of Series B stock has the economic rights equivalent
     to 1,000 shares of common stock subject to antidilution adjustments. The
     rights will convert into the shares of Series B stock upon the receipt of
     antitrust clearance under the Hart-Scott-Rodino Antitrust Improvements Act
     of 1976. The Series B stock will convert into restricted shares of
     underlying common stock of Dime upon, among other events, distribution of
     the litigation tracking warrants that Dime has assumed it will distribute
     to all other stockholders. (The litigation tracking warrants are described
     below.) The aggregate purchase price Warburg delivered to us at the first
     closing was approximately $210 million. At the first closing, Warburg also
     was given warrants to purchase 8,142.738 shares of Series C junior
     nonvoting preferred stock and warrants to purchase 3,866.753 shares of
     Series D junior nonvoting preferred stock, each series referencing 1,000
     shares of Dime's common stock per share of the series.
                                       10
<PAGE>   14

          Second Closing.  Upon receipt of other necessary regulatory approvals,
     including a determination by the Office of Thrift Supervision that Warburg
     does not control us, Warburg will purchase, for approximately $28 million,
     1,598.173 additional shares of Series B stock and additional warrants to
     purchase approximately 1,598.173 shares of Series D stock.

     One way to think of the aggregate purchase price paid by Warburg is that
Warburg is paying a price of $17.50 for the economic equivalent of one share of
common stock and a warrant to purchase the economic equivalent of another share
at an exercise price of $21.50, with such shares and warrants subject to a
number of conditions, limits and rights.

     Our financial advisors, Credit Suisse First Boston and Merrill Lynch,
performed analyses of the securities Warburg is buying to assist us in
evaluating and considering the investment and presented their analyses to our
board of directors. Both Credit Suisse First Boston and Merrill Lynch are
internationally recognized investment banking firms that were selected by Dime
to advise us in connection with the North Fork offer based on their reputations
and experience. As part of their engagement, they assisted us with our strategic
review and, in particular, the transaction with Warburg. Both firms are familiar
with Dime, having worked on several engagements in recent years.

     Our advisors concluded that, based on the market price of our common stock
at the time that Warburg agreed to make the investment, Warburg is receiving
securities valued between $16.40 and $18.45 per underlying common share and
related warrant. We refer to this as the "per share value" of Warburg's
investment. We think this value compares favorably to the price of $17.50 per
share and warrant Warburg is paying and suggests that Warburg is paying values
consistent with the market value of our common stock at the time of its
investment. To help you evaluate Warburg's investment, we provide some of the
details of our financial advisors' analyses below. These analyses and estimates
can vary greatly because they are based on a number of judgments and assumptions
regarding financial, economic and market matters that are uncertain and beyond
our control. Accordingly, if you have any questions regarding the effects of
Warburg's investment on your decision to tender, you may want to consult your
own financial advisor.

          Market Price of Common Stock.  Our financial advisors began their
     analysis with the market price of our common stock and noted that the
     average closing price for the five trading days before we announced
     Warburg's investment was $16.60.

          Transfer Restrictions and Illiquidity.  Next, our financial advisors
     considered the effect of the transfer restrictions that Warburg agreed to,
     as well as the large size of the equity investment. They noted that the
     transfer restrictions and the large percentage of the trading volume that
     the investment represents should generally reduce the value of the
     securities received by Warburg. They estimated that these transfer
     restrictions reduced the per share value to Warburg of its investment by
     about 10% to 15% of the average market price of our common stock, or $1.66
     to $2.49. Our financial advisors based these estimates on their market
     experience, although there were no directly comparable public valuations.
     Other financial analysts may value these transfer restrictions differently,
     which would change the estimated per share value of Warburg's investment.
     For your reference, the transfer restrictions are summarized below.

          Warrants.  Using the Black-Scholes method for valuing options, our
     advisors then estimated the value of the warrants we are issuing to
     Warburg. To do so, our financial advisors made several important
     assumptions. In particular, they assumed a longer-term volatility in our
     common stock of between 25% and 35% and reduced the value of the warrants
     because the large amount of stock covered by them would likely be illiquid
     and to give effect to the transfer restrictions Warburg has agreed to. As a
     result, our advisors estimated that the warrants increased the per share
     value to Warburg of its investment by between $2.83 and $4.05. The terms of
     the warrants are summarized below.

          You should note that the volatility our advisors assumed is lower than
     the short-term volatility implied by the price of publicly traded options
     in our stock at the time Warburg agreed to make the

                                       11
<PAGE>   15

     investment (and lower than the volatility Warburg and we agreed to use to
     calculate a purchase price if we are required by the Investment Agreement
     to buy back the warrants from Warburg in the event of a change of control).
     Our advisors believe the lower volatility is appropriate in light of the
     differential in risk associated with the significantly longer time period
     of the warrants (7 years) relative to publicly traded options (less than 1
     year). The per share value of Warburg's investment would be increased (and
     the value of the investment from the perspective of Dime would be
     decreased) if you used a higher volatility and/or a smaller adjustment for
     the illiquidity of the underlying stock.

          Litigation Tracking Warrants.  Finally, our advisors considered that
     Warburg has agreed to give up the right to receive the litigation tracking
     warrants that we intend to issue. Based on the trading value of comparable
     securities issued by other thrifts, our financial advisors estimated that
     giving up the litigation tracking warrants decreased the per share value
     Warburg received by about $0.54. Although we intend to issue litigation
     tracking warrants as we have proposed, neither we nor our advisors can
     guarantee when we will issue litigation tracking warrants or the prices at
     which they will trade.

          Other.  Our advisors considered other aspects of Warburg's investment,
     many of which are intangible, but did not assign a specific financial value
     to them because they did not believe it was possible or meaningful to
     attempt to do so. These included Warburg's agreement to limit its purchases
     of our common stock and not to acquire control of us, Warburg's right to
     put the warrants back to us if certain change in control events were to
     occur, our agreement to appoint or elect one Warburg representative to our
     board of directors, regulatory and market issues, and the fact that none of
     Warburg's securities is currently convertible into common stock. Some of
     these factors could be considered to be favorable to Warburg and some of
     them could be considered to be unfavorable. In addition, our advisors noted
     that they were not expressing any view as to the merits of the Warburg
     investment relative to any alternative business strategies or the effect of
     any other transaction in which we might engage.

     As discussed in Section 16, our advisors are receiving compensation in
connection with the Warburg transaction and this tender offer.

     To comply with regulatory requirements, Warburg's investment has been
structured using several different securities. If all the securities purchased,
and to be purchased, by Warburg were to be converted today into shares of Dime's
common stock, they would amount to approximately 27.2 million shares, or
approximately 24.9%, of the outstanding common stock, before giving effect to
the new issuance of shares of common stock underlying the convertible
securities. None of the securities is in fact convertible into common stock at
this time. The material terms of these securities are described below.

          Series B Stock.  Each share of Series B stock is entitled to 1,000
     votes on all matters on which shares of Dime's common stock are entitled to
     vote, together with the common stock as a single class. Shares of Series B
     stock are entitled to receive dividends the same as those paid on 1,000
     shares of Dime's common stock, other than the distribution of litigation
     tracking warrants. In case of a merger or similar transaction, shares of
     Series B stock will be exchanged into equivalent securities of the
     acquiring company. Shares of Series B stock will convert into shares of
     Dime's common stock on the earliest of (1) the issuance of the litigation
     tracking warrants, (2) a change in control of Dime, (3) lapsing of the
     transfer restrictions placed on the securities under certain provisions of
     the Investment Agreement (for example, if we breach our material
     obligations in the Investment Agreement), or (4) April 6, 2001.

          Warburg does not currently own any shares of Series B stock. When the
     rights to purchase Series B stock acquired by Warburg are converted,
     Warburg will be entitled to (1) receive all dividends and distributions as
     if it owned the Series B stock on July 6 and (2) vote the shares of Series
     B stock on all matters on which they are entitled to vote.

                                       12
<PAGE>   16

          Series C Stock.  Shares of Series C stock are not entitled to vote,
     except as required by law. Shares of Series C stock are entitled to receive
     dividends, other than the distribution of litigation tracking warrants, the
     same as those paid on 1,000 shares of Dime's common stock. In case of a
     merger or similar transaction, shares of Series C stock will be exchanged
     into equivalent securities of the acquiring company. Upon the receipt of
     (1) written advice of counsel that, under applicable federal banking laws,
     the shares of Series C stock may be converted or (2) a certificate that
     Warburg is transferring the shares pursuant to a widely dispersed sale,
     shares of Series C stock are convertible into shares of Dime's common
     stock, unless the Series B stock has not yet converted into common stock,
     in which case, the shares of Series C stock will be convertible only into
     shares of Series B stock.

          Warburg does not currently own any shares of Series C stock, but owns
     only warrants to purchase shares of Series C stock.

          Series D Stock.  Shares of Series D stock are not entitled to vote,
     except as required by law. Shares of Series D stock are entitled to receive
     dividends, other than the distribution of litigation tracking warrants, the
     same as those paid on 1,000 shares of Dime's common stock. In case of a
     merger or similar transaction, shares of Series D stock will be exchanged
     into equivalent securities of the acquiring company. The Series D stock
     will not be convertible into any other class of stock of Dime unless Dime
     receives stockholder approval of the issuance of over 20% of its common
     stock or equivalents under NYSE rules. Upon such approval, the Series D
     stock will convert into Series C stock. The Series C stock may then be
     converted into Series B stock or Dime's common stock if the conversion of
     the Series C stock or Series B stock has already occurred. We have agreed
     to use our reasonable best efforts to obtain this stockholder approval
     prior to September 30, 2002.

          Warburg does not currently own any shares of Series D stock, but owns
     only warrants to acquire Series D stock.

          Warrants.  The Series C and Series D warrants will allow Warburg to
     purchase Series C stock and Series D stock at an exercise price of $21.50
     per underlying common share, subject to a number of antidilution and other
     adjustments. All the warrants issued to Warburg expire seven years after
     issuance. None of the warrants has any voting rights.

          As with the underlying Series C stock, the Series C warrants will be
     exchanged when it is permissible for Dime to do so under the federal
     banking laws and regulations or in the event that Warburg intends to
     transfer the warrants in a widely dispersed sale. At such time, the Series
     C warrants will be exchanged for Series B warrants if the Series B stock
     has not yet converted into shares of Dime's common stock. Otherwise, the
     Series C warrants will be converted into warrants to purchase Dime's common
     stock.

          As with the underlying Series D stock, the Series D warrants will be
     exchanged for Series C warrants upon the requisite approval by Dime's
     stockholders under NYSE rules.

          We have a right of first offer on any sale of warrants by Warburg.
     Warburg may also put any warrants to us (pursuant to an agreed valuation
     methodology) upon the occurrence of certain change in control events and
     may put Series D warrants to us (pursuant to an agreed valuation
     methodology) if the appropriate stockholder approval under NYSE rules is
     not obtained by September 30, 2003 or the other transfer restrictions on
     the warrants lapse before then. The agreed valuation methodology will
     involve a calculation using the Black-Scholes method for valuing options.
     The assumptions to be used for this calculation include: a volatility rate
     of 40% (or 30% for a put of the Series D warrants under the separate
     put-triggering events for the Series D warrants), a dividend yield of 1.9%
     and an interest rate of 6.25%. The exercise price will be assumed to be the
     exercise price of the warrant at the occurrence of the event allowing the
     put and the term of the warrant will be the remaining term of the warrant
     from the date of that event. For purposes of acquisition transactions
     causing a change in control, the underlying security price for the
     calculation will reference the price to be paid per share in the
     acquisition transaction; for other events permitting the put, the
     underlying security price

                                       13
<PAGE>   17

     will be based on the 5-day average closing market price for Dime's common
     stock immediately after the event.

          In addition to customary antidilution provisions for the warrants, we
     have agreed to additional antidilution protections in two circumstances.
     First, although the various series of stock that Warburg may acquire upon
     exercise of the warrants do not have the right to receive litigation
     tracking warrants, the exercise price of the warrants may be adjusted if
     the average aggregate market price of the litigation tracking warrants is
     over $100 million for an agreed period of time after the issuance of the
     litigation tracking warrants. In this case, the exercise price of the
     warrants will be adjusted downward for the aggregate market price over $100
     million, but only in proportion to Warburg's ownership of Dime. Second, the
     exercise price of the warrants may be adjusted downward, in proportion to
     Warburg's ownership of Dime, for any payment potentially made by us to
     Hudson United Bancorp in excess of $15 million under the Termination,
     Option Cancellation and Settlement Agreement, dated April 28, 2000, between
     us and Hudson regarding the termination of the then-pending merger between
     us and Hudson, unless the payment relates to (1) a breach of
     representations by Warburg regarding its ownership of Dime or (2) another
     subsequent transaction, such as a merger or tender offer, approved or
     recommended by our board of directors.

     The Investment Agreement contains a number of other material provisions,
which are summarized below.

          Standstill Agreement.  Until July 6, 2003, Warburg has agreed that it
     will not purchase or acquire any shares of Dime's common stock that would
     result in its having control over us or owning in excess of 24.9% of our
     outstanding voting shares. In addition, Warburg has agreed that it will not
     take any action that would violate its standard agreement with the Office
     of Thrift Supervision to refrain from controlling us.

          Voting.  Each share of Series B stock will be entitled to the same
     voting rights as, and will vote together with, shares of Dime's common
     stock (subject to each share of Series B stock representing the equivalent
     of 1,000 shares of common stock). Warburg will not be entitled to vote its
     shares until it exercises the rights to purchase Series B stock or until it
     exercises any Series B warrants that may be issued on conversion of Series
     C warrants or Series D warrants, at which time it will become a holder of
     Series B stock. Warburg has not entered into any voting agreement with us.

          Preemptive Rights.  As long as Warburg owns at least 5% of the
     outstanding shares of Dime's common stock (assuming the exercise of all
     outstanding options and warrants and conversion of convertible preferred
     stock), if Dime issues any common stock after the date of the investment,
     Warburg has the right to purchase from Dime that amount of shares required
     for it to maintain its proportionate interest in Dime. To the extent
     Warburg utilizes this right to maintain its percentage ownership interest,
     it will not be entitled to duplicative protection of antidilution
     adjustments under the terms of the warrants.

          Governance Matters.  We have agreed to elect or appoint one person
     nominated by Warburg to serve as a director of Dime and its wholly owned
     subsidiary, The Dime Savings Bank of New York, FSB. In addition, two
     Warburg representatives will be allowed to attend and observe meetings of
     the boards of directors of Dime and Dime Savings Bank, including meetings
     of any committees, but excluding executive sessions of the boards of
     directors.

          Warburg will relinquish the right to its board seat and will lose one
     observer upon the sale or distribution of 75% or more of its shares of
     Dime's common stock (or securities representing common stock). In addition,
     Warburg has agreed to relinquish its right to a board seat, but retain the
     right to two observers, upon conversion by us to a bank holding company
     (should such conversion occur), if such action is necessary to satisfy
     Federal Reserve Board requirements. In such case, however, Warburg will be
     afforded the option of selling down its interest in Dime or taking other
     measures to reduce its voting interest in Dime and retain its board seat.

                                       14
<PAGE>   18

          We have appointed Mr. Howard H. Newman, managing director of Warburg,
     as a director of Dime, effective upon receipt of antitrust clearance under
     the Hart-Scott-Rodino Act for Warburg's investment. Additionally, Mr.
     Newman has been appointed as a director of Dime Savings Bank effective upon
     the increase of Dime Savings Bank's board size in accordance with
     regulations of the Office of Thrift Supervision.

          Transfer Restrictions.  With certain exceptions, shares of stock and
     warrants owned by Warburg will be restricted from transfer subject to,
     among other things, a schedule whereby 20% of the shares will be freely
     tradeable after one year; an additional 30% will be freely tradeable after
     two years; and the balance will be freely tradeable after three years. In
     addition, Warburg will be permitted to tender into tender or exchange
     offers (1) on a pro rata basis with other stockholders, provided at least
     60% of the shares sought in the tender or exchange offer have been tendered
     by Dime's other stockholders or (2) not opposed by us.

          Warburg will be released from the transfer restrictions if, among
     other things, (1) antitrust clearance under the Hart-Scott-Rodino Act is
     not received in six months, (2) we breach our material obligations in the
     Investment Agreement, or (3) we execute documentation, or recommend an
     offer to stockholders, that would result in a change in control of Dime.

          We have agreed to register the securities acquired by Warburg as the
     transfer restrictions expire.

     NEW CHAIRMAN.  Mr. Anthony P. Terracciano has been elected Chairman of our
board of directors and a director of Dime Savings Bank. In addition, he is
entering into an employment agreement whereby he will be advising us on
strategic issues. See Section 11. His career includes service as Vice Chairman
of Chase Manhattan Bank, President and Chief Operating Officer of Mellon Bank,
Chairman, President and Chief Executive Officer of First Fidelity and, following
the sale of that company to First Union Corporation, President of First Union.

     AMENDMENTS TO STOCKHOLDER PROTECTION RIGHTS AGREEMENT. In order to
demonstrate our willingness to consider a sale strategy at the right time and on
the right terms, our board of directors has amended the rights agreement in two
material respects. First, the rights agreement will not apply to a tender offer
that has at least a 50% cash component for all shares and sufficient liquidity
in any securities component, provided that the offer is accepted by the
beneficial owners of at least 75% of our common stock. Second, a "sunset"
provision has been added to the rights agreement so that it will terminate
immediately following our 2002 annual stockholders' meeting. We have reserved
the right to adopt other similar stockholder rights plans in the future should
our board of directors decide it is in the best interests of us and our
stockholders.

     The rights agreement was also amended to permit Warburg and its affiliates
to purchase securities under and in accordance with the Investment Agreement
without triggering the rights agreement protections.

     The other provisions of the rights agreement are described more fully in
Section 8 of this document.

     LITIGATION TRACKING WARRANTS AND OUR GOODWILL LAWSUIT. We currently intend
to distribute litigation tracking warrants to our common stockholders
representing the right to receive, upon exercise of the litigation tracking
warrants, shares of our common stock equal in value to 85 percent of the net
after-tax proceeds, if any, from our pending goodwill lawsuit against the United
States government. Under the terms of Warburg's Investment Agreement, Warburg
will not receive any of the litigation tracking warrants.

     OTHER INITIATIVES.  As part of our ongoing effort to improve our growth
rate and the quality of our earnings, we will be conducting a detailed review of
our business plan intended to identify opportunities to build further momentum
in revenue-producing activities and make additional investments in technology.
We believe these opportunities will include expansion of our business banking
activities and development of more comprehensive e-commerce offerings. In
addition, we are reviewing our expense infrastructure in order to reduce costs
and are considering various balance sheet restructuring initiatives, including a
potential sale of a substantial portion of our portfolio of investment
securities.

                                       15
<PAGE>   19

     NORTH FORK'S HOSTILE OFFER.  On March 5, 2000, North Fork announced an
unsolicited hostile offer for all the issued and outstanding shares of common
stock of Dime in exchange for 0.9302 shares of North Fork common stock and $2.00
in cash per Dime common share. On March 15, 2000, North Fork officially
commenced its hostile offer.

     On March 19, 2000, our board of directors rejected North Fork's hostile
offer as inadequate and subsequently distributed to Dime stockholders a
solicitation/recommendation statement on Schedule 14D-9 explaining the many
reasons for the board's rejection of North Fork's hostile offer. The Schedule
14D-9 also included opinions of our financial advisors, Credit Suisse First
Boston and Merrill Lynch, that North Fork's hostile exchange offer is inadequate
from a financial point of view to our stockholders. The Schedule 14D-9, as filed
with the SEC on March 21, 2000 and as amended from time to time, is incorporated
by reference into this document. North Fork has also entered into an agreement
with Fleet Boston Corporation to finance the cash portion of its hostile offer.
Pursuant to this agreement, Fleet Boston will acquire preferred stock and
warrants to purchase common stock of North Fork in exchange for $250 million.

     Conditions to North Fork's Hostile Offer.  North Fork's hostile offer
remains subject to a number of conditions described in the prospectus and
registration statement distributed to stockholders in connection with North
Fork's hostile offer. Some of these conditions include:

     - Dime's stockholders having validly tendered and not withdrawn prior to
       the expiration of North Fork's hostile offer that number of shares of
       Dime common stock which, together with the shares of Dime common stock
       beneficially owned by North Fork for its own account, constitutes a
       majority of the shares of Dime common stock outstanding on a fully
       diluted basis,

     - Dime having entered into a definitive merger agreement with North Fork to
       provide for the acquisition of Dime pursuant to North Fork's hostile
       offer and the proposed Dime-North Fork merger,

     - North Fork's stockholders approving the issuance of North Fork common
       stock pursuant to North Fork's hostile offer and the proposed Dime-North
       Fork merger under applicable NYSE rules,

     - North Fork being satisfied, in its sole judgment, that Dime's rights
       agreement and Delaware General Corporation Law Section 203 do not apply
       to North Fork's hostile offer and the proposed Dime-North Fork merger,

     - All regulatory approvals required to consummate North Fork's hostile
       offer and the proposed Dime-North Fork merger having been obtained and
       remaining in full force and effect without the imposition of any
       condition or restriction that would be materially adverse to North Fork
       and Dime on a combined basis, and all statutory waiting periods in
       respect thereof having expired, including those of the Federal Reserve
       Board and the Department of Justice,

     - Dime not having entered into or effectuated any other agreement or
       transaction with any person or entity having the effect of impairing
       North Fork's ability to acquire Dime or otherwise diminishing the
       expected economic value to North Fork of the acquisition of Dime, and

     - The absence of any pending suit, action or proceeding by any governmental
       entity challenging North Fork's hostile offer, seeking to restrain or
       prohibit North Fork's ownership or operation of Dime, seeking to prohibit
       effective control by North Fork in any material respect over the business
       operations of Dime or that would otherwise be reasonably likely to have a
       material adverse effect on North Fork or Dime.

     North Fork has stated that there can be no assurance as to whether the
conditions to its hostile offer will be satisfied and, if so, as to the timing
of satisfaction of such conditions. To our knowledge, these conditions have not
yet been satisfied or waived by North Fork. Also, satisfaction of a number of
these conditions is contingent upon cooperation by us and we have rejected North
Fork's hostile offer as inadequate.

                                       16
<PAGE>   20

     Status of Hostile Offer.  On July 28, 2000, North Fork announced that about
18.5 million shares of Dime common stock had been tendered into its hostile
offer representing approximately 17% of the shares outstanding on that date,
before giving effect to the Warburg investments. Unless further extended, North
Fork's hostile offer is currently scheduled to expire on September 29, 2000.

     Dime has not engaged in discussions with North Fork regarding the terms of
its hostile offer. We have, however, identified to North Fork, by way of our
Schedule 14D-9, a variety of substantive issues for North Fork to consider.

     North Fork's Proxy Solicitation.  In connection with Dime's annual meeting
of stockholders held on July 14, 2000, Dime solicited proxies for the election
of five director nominees. North Fork solicited proxies from Dime stockholders
to vote "withhold authority" for Dime's director nominees. On July 28, 2000,
results of the vote for Dime's director nominees were certified by the
independent inspector of elections and indicated that holders of 70% of the
shares represented at the annual meeting withheld authority for Dime's director
nominees.

     On July 14, 2000, North Fork filed suit in the Court of Chancery of the
State of Delaware in and for New Castle County against Dime and several of
Dime's directors. The suit requested equitable relief such that the five Dime
directors nominated for election at Dime's 2000 annual meeting of stockholders
would have the status of holdover directors and that such directors should be up
for election no later than Dime's 2001 annual meeting of stockholders. On July
24, 2000, certain stockholders of Dime filed a similar suit in the Court of
Chancery of the State of Delaware.

     North Fork has indicated publicly that it plans to propose a slate of
directors for Dime's board at the 2001 annual meeting of stockholders.

     Other Litigation.  We and North Fork are engaged in litigation over various
matters related to North Fork's hostile offer, including our suit against North
Fork alleging false and misleading statements in documents distributed by North
Fork to stockholders, our suit against North Fork alleging anticompetitive
effects of a combined Fleet Boston-North Fork-Dime in Suffolk County, New York
and North Fork's suit against us for alleged false and misleading statements in
documents sent by us to stockholders. This, and other related litigation, is
discussed more fully in our Quarterly Report on Form 10-Q for the quarter ended
March 31, 2000, which is incorporated by reference into this document. In
addition, the Department of Justice served a civil investigative demand on Dime,
North Fork and Fleet Boston with regard to its analysis of issues concerning a
combination of these three entities. We believe that the Department of Justice
continues to consider these issues and collect and analyze documents under this
demand.

     PURPOSES OF OUR OFFER.  Given the newly announced initiatives, we believe
that stockholder value will be enhanced and that investment in our common stock
is a valuable investment opportunity. We are initiating our offer to enable you
to decide whether you desire to continue to be invested in Dime alongside
Warburg and Mr. Terracciano and take part in our new initiatives or whether you
desire to obtain current value for your shares. In addition, we are making our
offer for the following reasons:

     - Our offer for between $16.00 and $18.00 per share presents a value to
       stockholders comparable to the current market value of North Fork's
       hostile offer, but offers it completely in cash. Those stockholders who
       desire to recognize that cash value may choose to tender into our offer.
       The reasons we believe North Fork's offer is unlikely to close any time
       soon were explained in detail in the Schedule 14D-9 we distributed to
       stockholders on March 21, 2000. Stockholders should be aware, however,
       that the tax consequences of receiving cash in our offer are different
       from those resulting from North Fork's hostile offer. See Section 14 for
       information regarding the tax consequences of our offer.

       As of July 28, 2000, North Fork's hostile offer had a price of $16.42
       given the closing price of North Fork's common stock on that date.
       Because North Fork's offer is comprised mostly of shares of North Fork
       common stock, its value will fluctuate based on the daily market prices
       of those shares. We urge you to obtain more current market quotations for
       this stock.

                                       17
<PAGE>   21

In addition, as explained more fully in the Schedule 14D-9, we believe that the
value of North Fork's hostile offer is uncertain and subject to a number of
risks. The Schedule 14D-9 is incorporated by reference into this document.

     - We believe our offer is a method by which we can maintain or increase
       stockholder value while permitting an important investor to provide us
       capital. We have issued, and will be issuing, securities to Warburg
       representing an interest in our common stock. The Series B stock
       purchased, and to be purchased, by Warburg indirectly represents
       13,607,664 shares of underlying common stock. We believe that a prudent
       use of the additional capital given to us by Warburg is to purchase our
       common stock and maintain a consistent number of shares in the market
       while attempting to increase stockholder value through our newly
       announced initiatives.

     - We believe that our common stock is undervalued in the market place at
       this time based on prior pricing parameters.

     EFFECTS OF THE OFFER.  As we described above, we are in the process of
issuing preferred stock and warrants to Warburg. If both that investment and
this offer are fully completed, the preferred stock issued to Warburg should
offset the stock purchased in this offer. Accordingly, if you do not tender,
your percentage ownership interest in Dime after the offer should be about the
same as your percentage ownership interest before Warburg's investment.

     Of course, we may issue additional shares of common stock and other
securities at any time, and these issuances will reduce your percentage
ownership interest. For example, we are also giving warrants to Warburg. If
Warburg exercises these warrants and pays the exercise price, your percentage
ownership interest will decrease. The exercise price of Warburg's warrants is
currently $21.50 per underlying common share. As we discuss below, we also may
purchase more of our stock, which would have the effect of increasing your
percentage ownership interest.

     As we discuss above, one way to think about Warburg's investment in us is
that, for a price of $17.50, we are selling Warburg the economic equivalent of
one share of common stock and a warrant to purchase the economic equivalent of
another share at an exercise price of $21.50. Depending on the selected purchase
price in this offer and how one values the warrants, the other contractual
provisions we have given Warburg and the contractual provisions Warburg has
given us, the effective price per common stock equivalent paid by Warburg may be
more or less than the purchase price in this offer.

     You may be able to sell shares that you do not tender or that are otherwise
not purchased in our offer on the NYSE or otherwise. We can not predict or
assure you, however, as to the price at which you will be able to sell your
shares, which may be higher or lower than the purchase price paid by us in this
offer.

     We do not have any current plans to purchase more shares of our common
stock. We may, however, do so in the future through purchases in the open
market, private transactions or other tender offers or through any other means.
Future purchases may be on terms that are more or less favorable to stockholders
than this offer. However, SEC Rules 14e-5 and 13e-4 generally prohibit us and
our affiliates from purchasing any shares outside of our offer until ten
business days after the expiration date of our offer, although there are some
exceptions. Any future purchases will depend on many factors, which include
market conditions and the condition of our business.

     Shares that we acquire in our offer will be retained as treasury stock, and
will be available for us to issue without further stockholder action (except as
required by applicable law or the rules of the NYSE or any other securities
exchange on which the shares are listed) for purposes including, without
limitation, acquisitions, raising additional capital and the satisfaction of
obligations under existing or future employee benefit or compensation programs
or stock plans or compensation programs for directors.

     NEITHER WE NOR OUR BOARD OF DIRECTORS, NOR THE INFORMATION AGENT, NOR
EITHER OF THE DEALER MANAGERS MAKES ANY RECOMMENDATION TO ANY STOCKHOLDER AS TO
WHETHER TO TENDER OR NOT TENDER ANY SHARES OR AS TO THE PRICE OR PRICES AT WHICH
STOCKHOLDERS MAY CHOOSE TO TENDER THEIR SHARES. WE HAVE NOT AUTHORIZED ANY
PERSON TO MAKE ANY SUCH RECOMMENDATION. STOCKHOLDERS SHOULD CAREFULLY EVALUATE
ALL INFORMATION IN OUR

                                       18
<PAGE>   22

OFFER, CONSULT THEIR OWN INVESTMENT AND TAX ADVISORS, AND MAKE THEIR OWN
DECISIONS ABOUT WHETHER TO TENDER SHARES AND, IF SO, HOW MANY SHARES TO TENDER
AND THE PRICE OR PRICES AT WHICH TO TENDER. WE HAVE BEEN INFORMED THAT NONE OF
OUR DIRECTORS OR EXECUTIVE OFFICERS INTENDS TO TENDER ANY SHARES IN THE TENDER
OFFER.

     OTHER TRANSACTIONS.  Except as described in this document, we currently
have no plans, proposals or negotiations that relate to or would result in:

     - an extraordinary transaction, such as a merger, reorganization or
       liquidation, involving us or any of our subsidiaries,

     - a purchase, sale or transfer of an amount of our assets or any of our
       subsidiaries' assets that would be material to us and our subsidiaries
       taken as a whole,

     - a material change in our present dividend rate or policy, or in our
       indebtedness or capitalization,
     - any class of our equity securities being delisted from the NYSE or
       ceasing to be authorized to be quoted in an automated quotations system
       operated by a national securities association,

     - any class of our equity securities becoming eligible for termination of
       registration under the Securities Exchange Act of 1934,

     - a suspension of our obligation to file reports under the Exchange Act,

     - a change in our present board of directors or management,

     - a material change in our corporate structure or business,
     - an acquisition or disposition by any person of our securities, or

     - a change in our certificate of incorporation, by-laws or other governing
       documents or an action that could impede the acquisition of control of
       us.

     Although we do not currently have any plans, other than as described in
this document, that relate to or would result in any of the events discussed
above, as we continue to evaluate opportunities for increasing stockholder value
we may undertake or plan actions that relate to or could result in one or more
of these events.

SECTION 3.  PROCEDURES FOR TENDERING SHARES.

     PROPER TENDER OF SHARES.  For your shares to be properly tendered, either
(1) or (2) below must happen:

     (1) The depositary must receive all of the following before or on the
         expiration date at the depositary's address on the back page of this
         document:

        - one of (a) the certificates for the shares (b) a confirmation of
          receipt of the shares pursuant to the procedure for book-entry
          transfer we describe below or (c) in the case of shares held in our
          dividend reinvestment program, completion of the appropriate sections
          of the letter of transmittal, and

        - one of (a) a properly completed and executed letter of transmittal or
          a manually executed facsimile of it, including any required signature
          guarantees, (b) an "agent's message" of the type we describe below in
          the case of a book-entry transfer or (c) a specific acknowledgement in
          the case of a tender through the "automated tender offer program" we
          describe below, and

        - any other documents required by the letter of transmittal.

     (2) You must comply with the guaranteed delivery procedure set forth below.

                                       19
<PAGE>   23

     In accordance with Instruction 5 of the letter of transmittal, if you want
to tender your shares you must properly complete the pricing section of the
letter of transmittal, which is called "Price At Which You Are Tendering":

     - If you wish to maximize the chance that your shares will be purchased at
       the purchase price determined by us, you should check the box in this
       section of the letter of transmittal next to "Shares tendered at price
       determined pursuant to the offer." This means that you will accept the
       purchase price selected by us in accordance with the terms of our offer.
       Note that this election could result in your shares being purchased at
       the minimum price of $16.00 per share.

     - If you wish to indicate a specific price (in multiples of $0.125) at
       which your shares are being tendered, you must check ONE box in this
       section under "Shares tendered at a price determined by you." You should
       be aware that this election could mean that none of your shares will be
       purchased if you choose a price that is higher than the purchase price we
       eventually select after the expiration date.

     If you want to tender portions of your shares at different prices you must
complete a separate letter of transmittal for each portion of your shares that
you want to tender at a different price. However, the same shares cannot be
tendered (unless properly withdrawn previously in accordance with Section 4) at
more than one price. To tender shares properly, one and only one price box must
be checked in the "Price At Which You Are Tendering" section on each letter of
transmittal.

     In addition, odd lot holders who tender all shares must complete the
section captioned "Odd Lots" in the letter of transmittal and, if applicable, in
the notice of guaranteed delivery, to qualify for the preferential treatment
available to odd lot holders as set forth in Section 1.

     If you tender your shares directly to the depositary, you will not need to
pay any brokerage commissions. If you hold shares through a broker or bank,
however, you should ask your broker or bank to see if you will be charged a fee
to tender your shares through the broker or bank.

     Participants in the Retirement 401(k) Investment Plan of Dime or the North
American Mortgage Company Retirement and 401(k) Savings Plan who wish to tender
some or all of the shares allocated to their accounts must follow the procedures
in either the "Letter to Participants in the Retirement 401(k) Investment Plan
of Dime Bancorp, Inc." or the "Letter to Participants in the North American
Mortgage Company Retirement and 401(k) Savings Plan," as applicable, and return
your instructions to the appropriate trustee or tabulating agent. Each of these
letters has been provided separately to appropriate 401(k) savings plan
participants. Your instructions must be received by the appropriate trustee or
tabulating agent no later than five business days before the expiration date or
no shares allocated to your account will be tendered.

     Participants in our dividend reinvestment program should follow the
instructions in the letter of transmittal to tender properly shares held in
their program account.

     ENDORSEMENTS AND SIGNATURE GUARANTEES.  Depending on how your shares are
registered and to whom you want payments or deliveries made, you may need to
have your certificates endorsed and the signatures on the letter of transmittal
and endorsement guaranteed by an "eligible guarantor institution," as such term
is defined in Rule 17Ad-15 under the Exchange Act. No endorsement or signature
guarantee is required if:

     - the letter of transmittal is signed by the registered holder of the
       shares tendered (which, for purposes of this Section 3, includes any
       participant in The Depository Trust Company, referred to as the
       "book-entry transfer facility," whose name appears on a security position
       listing as the owner of the shares) exactly as the name of the registered
       holder appears on the certificate(s) for the shares and payment and
       delivery are to be made directly to the holder, unless the holder has
       completed either the box captioned "Special Delivery Instructions" or the
       box captioned "Special Payment Instructions" on the letter of
       transmittal; or

                                       20
<PAGE>   24

     - shares are tendered for the account of a bank, broker, dealer, credit
       union, savings association or other entity that is a member in good
       standing of the Securities Transfer Agents Medallion Program or a bank,
       broker, dealer, credit union, savings association or other entity that is
       an eligible guarantor institution.

See Instruction 1 of the letter of transmittal.

     On the other hand, if a certificate for shares is registered in the name of
a person other than the person executing a letter of transmittal or you are
completing either the box captioned "Special Delivery Instructions" or the box
captioned "Special Payment Instructions" on the letter of transmittal, then

     - your certificates must be endorsed or accompanied by an appropriate stock
       power, in either case signed exactly as the name of the registered holder
       appears on the certificates, and

     - the signature on (1) the letter of transmittal and (2) on your
       certificates or stock power must be guaranteed by an eligible guarantor
       institution.

     METHOD OF DELIVERY.  Payment for shares tendered and accepted for payment
under our offer will be made only after timely receipt by the depositary of all
of the following:

     - certificates for such shares, a timely confirmation of the book-entry
       transfer of such shares into the depositary's account at the book-entry
       transfer facility as described below or, in the case of shares held in
       our dividend reinvestment program, completion of the appropriate sections
       of the letter of transmittal,

     - any of a properly completed and duly executed letter of transmittal or a
       manually signed facsimile thereof, an agent's message in the case of a
       book-entry transfer or the specific acknowledgement in the case of a
       tender through the automated tender offer program, and

     - any other documents required by the letter of transmittal.

     THE METHOD OF DELIVERING ALL DOCUMENTS, INCLUDING CERTIFICATES FOR SHARES,
THE LETTER OF TRANSMITTAL AND ANY OTHER REQUIRED DOCUMENTS, IS AT YOUR ELECTION
AND RISK. IF DELIVERY IS BY MAIL, REGISTERED MAIL WITH RETURN RECEIPT REQUESTED,
PROPERLY INSURED, IS RECOMMENDED.

     ALL DELIVERIES IN CONNECTION WITH OUR OFFER, INCLUDING A LETTER OF
TRANSMITTAL AND CERTIFICATES FOR SHARES, MUST BE MADE TO THE DEPOSITARY AND NOT
TO US, THE DEALER MANAGERS, THE INFORMATION AGENT OR THE BOOK-ENTRY TRANSFER
FACILITY. ANY DOCUMENTS DELIVERED TO US, THE DEALER MANAGERS, THE INFORMATION
AGENT OR THE BOOK-ENTRY TRANSFER FACILITY WILL NOT BE FORWARDED TO THE
DEPOSITARY AND THEREFORE WILL NOT BE DEEMED TO BE PROPERLY TENDERED. IN ALL
CASES, SUFFICIENT TIME SHOULD BE ALLOWED TO ENSURE TIMELY DELIVERY.

     BOOK-ENTRY DELIVERY.  The depositary will establish an account with respect
to the shares for purposes of our offer at the book-entry transfer facility
within two business days after the date of this document. Any institution that
is a participant in the book-entry transfer facility's system may make book-
entry delivery of the shares by causing the book-entry transfer facility to
transfer shares into the depositary's account in accordance with the book-entry
transfer facility's procedures for transfer. Even if delivery of shares is made
through a book-entry transfer into the depositary's account at the book-entry
transfer facility, either (1) or (2) below must occur:

     (1) The depositary must receive all of the following before or on the
         expiration date at the depositary's address on the back page of this
         document:

        - one of (a) a properly completed and executed letter of transmittal or
          a manually executed facsimile of it, including any required signature
          guarantees, (b) an agent's message as described below in the case of a
          book-entry transfer or (c) a specific acknowledgement in the case of a
          tender through the automated tender offer program, and

        - any other documents required by the letter of transmittal; or

     (2) The guaranteed delivery procedure described below must be followed.

                                       21
<PAGE>   25

     Delivery of the letter of transmittal or any other required documents to
the book-entry transfer facility does not constitute delivery to the depositary.

     The term "agent's message" means a message transmitted by the book-entry
transfer facility to, and received by, the depositary, which states that the
book-entry transfer facility has received an express acknowledgment from the
participant in the book-entry transfer facility tendering the shares that such
participant has received and agrees to be bound by the terms of the letter of
transmittal and that we may enforce such agreement against them.

     Participants in the book-entry transfer facility also may tender their
shares in accordance with the "automated tender offer program" to the extent it
is available to them for the shares they wish to tender. A stockholder tendering
through the automated tender offer program must expressly acknowledge that the
stockholder has received and agrees to be bound by the letter of transmittal and
that we may enforce such agreement against them.

     GUARANTEED DELIVERY.  If you want to tender your shares but your share
certificates are not immediately available or cannot be delivered to the
depositary before the expiration date, the procedure for book-entry transfer
cannot be completed on a timely basis, or if time will not permit all required
documents to reach the depositary before the expiration date, you can still
tender your shares, if all of the following conditions are satisfied:

     - the tender is made by or through an eligible guarantor institution;

     - the depositary receives by hand, mail, overnight courier or facsimile
       transmission, before the expiration date, a properly completed and duly
       executed notice of guaranteed delivery in the form we have provided with
       this document, specifying the price at which shares are being tendered,
       including (where required) a signature guarantee by an eligible guarantor
       institution in the form set forth in the notice of guaranteed delivery;
       and

     - all of the following are received by the depositary within three NYSE
       trading days after the date of receipt by the depositary of the notice of
       guaranteed delivery:

          - one of (a) the certificates for the shares, (b) a confirmation of
            receipt of the shares pursuant to the procedure for book-entry
            transfer we describe above or (c) in the case of shares held in our
            dividend reinvestment program, completion of the appropriate
            sections of the letter of transmittal, and

          - one of (a) a properly completed and executed letter of transmittal
            or a manually executed facsimile of it, including any required
            signature guarantees, (b) an "agent's message" of the type we
            describe above in the case of a book-entry transfer or (c) a
            specific acknowledgement in the case of a tender through the
            "automated tender offer program" we describe above, and

          - any other documents required by the letter of transmittal.

     401(K) SAVINGS PLANS.  If you are a participant in the Retirement 401(k)
Investment Plan of Dime or the North American Mortgage Company Retirement and
401(k) Savings Plan, you may instruct the trustee of your plan to tender some or
all of the shares allocated to your account by following the procedures in the
"Letter to Participants in the Retirement 401(k) Investment Plan of Dime
Bancorp, Inc." or the "Letter to Participants in the North American Mortgage
Company Retirement and 401(k) Savings Plan," as applicable, and returning it to
the appropriate trustee or tabulating agent. Each of these letters will be
furnished to you separately. In addition, all documents furnished to
stockholders generally in connection with the offer will be made available to
participants whose accounts under these 401(k) savings plans are credited with
shares. Participants in these 401(k) savings plans cannot use the letter of
transmittal to direct the tender of shares allocated to their account but must
use the separate instruction letter sent to them.

     These 401(k) savings plans are prohibited from selling shares to us for a
price that is less than the prevailing market price. Accordingly, if a
participant in either of these plans elects to tender shares at a

                                       22
<PAGE>   26

price that is lower than the prevailing market price of our common stock at the
expiration date, the tender price elected by the participant will be deemed to
have been increased to the closest tender price that is not less than the
closing price of our common stock on the NYSE on the expiration date. In
addition, our Benefits Committee, as a fiduciary for these 401(k) savings plans,
has the authority to revoke tender directions if it determines that sale of the
shares may not meet the standards of the Employee Retirement Income Security Act
of 1974.

     DELIVERY OF A LETTER OF TRANSMITTAL BY A 401(K) SAVINGS PLAN PARTICIPANT
DOES NOT CONSTITUTE PROPER TENDER OF HIS OR HER 401(K) SAVINGS PLAN SHARES.
PROPER TENDER CAN ONLY BE MADE BY THE APPROPRIATE TRUSTEE, WHO IS THE RECORD
OWNER OF THE SHARES HELD IN A 401(K) SAVINGS PLAN. PLEASE NOTE THAT INSTRUCTION
LETTERS MUST BE SUBMITTED TO THE APPROPRIATE TRUSTEE OR TABULATING AGENT AT
LEAST FIVE BUSINESS DAYS BEFORE THE EXPIRATION DATE. WE HAVE BEEN ADVISED THAT
IF THE APPROPRIATE TRUSTEE OR TABULATING AGENT HAS NOT RECEIVED A PARTICIPANT'S
INSTRUCTIONS AT LEAST FIVE BUSINESS DAYS BEFORE THE EXPIRATION DATE, THE TRUSTEE
WILL NOT TENDER ANY SHARES HELD ON BEHALF OF THE PARTICIPANT IN THE 401(K)
SAVINGS PLAN.

     The proceeds received from any tender of shares from a participant's 401(k)
savings plan account will be reinvested pro rata in accordance with the
participant's current investment directions for new contributions to that plan.
However, if the participant's current investment directions for new
contributions provide that some or all of the contributions are to be invested
in our common stock, then that portion of the tender proceeds will be invested
in a money market fund. Once the tender proceeds have been credited to the
participant's 401(k) savings plan account, the participant may reallocate his or
her investments among the various investment funds under the 401(k) savings plan
in the usual manner. Participants in the 401(k) savings plans are urged to read
their separate instruction letter and related materials carefully.

     DIVIDEND REINVESTMENT PROGRAM.  If you are a participant in our dividend
reinvestment program and you wish to tender shares held in your program account,
you must complete the box in the letter of transmittal entitled "Tender of
Shares Held in Dime Dividend Reinvestment and Optional Cash Purchase Program."
Shares credited to your program account under the dividend reinvestment program
will be tendered by EquiServe Trust Company, N.A., as administrator of the
program, according to the instructions provided in the appropriate places in the
letter of transmittal. As with the tender of other shares, shares in program
accounts for which the program administrator has not received timely
instructions prior to the expiration date of our offer will not be tendered. You
may direct that all or a portion of the shares held in your program account be
tendered by the program administrator.

     The dividend reinvestment program is available only to stockholders of
record. Accordingly, the participants in the dividend reinvestment program will
receive all documents furnished to stockholders generally in connection with the
offer. No additional documents will be delivered. You are urged to read the
letter of transmittal carefully.

     WITHDRAWAL OF SHARES FROM NORTH FORK'S HOSTILE OFFER.  IF YOU HAVE ALREADY
TENDERED YOUR SHARES TO NORTH FORK AND HAVE CHANGED YOUR MIND AND WISH TO TENDER
THEM TO US, YOU MUST PROPERLY WITHDRAW THEM FROM NORTH FORK'S HOSTILE OFFER
BEFORE YOU CAN TENDER THEM TO US. You may withdraw shares you tendered in North
Fork's hostile offer at any time before North Fork's hostile offer expires and
your shares are exchanged for North Fork stock and cash. To effectively
withdraw, North Fork's exchange agent must receive a written notice either at
one of the addresses listed below, or by facsimile at (201) 324-3402 or (201)
324-3403 (you may confirm your facsimile by telephone at (201) 222-4707). The
written notice must contain your name, address, social security number, the
number of shares you would like to withdraw, the certificate numbers of your
shares and the name of the registered holder of your shares, if different from
the person who tendered the shares. All signatures on the notice of withdrawal
must be guaranteed by a financial institution in accordance with the procedures
set forth in North Fork's prospectus under "The Offer-Withdrawal Rights." If
your shares have been tendered in North Fork's hostile offer through book-entry
tender procedures at The Depository Trust Company, the book-entry transfer
facility discussed in this document, a notice of withdrawal must also specify
the name and account number at The Depository Trust Company and otherwise comply
with The Depository Trust Company's procedures.

                                       23
<PAGE>   27

By Mail:

First Chicago Trust Company of New York
Attention: Corporate Actions
Suite 4660
P.O. Box 2569
Jersey City, NJ 07303-2569

By Hand:

First Chicago Trust Company of
New York
Attention: Corporate Actions
c/o Securities Transfer &
Reporting Services Inc.
100 William Street, Galleria
New York, NY 10038

By Overnight, Certified or
Express Mail Delivery:

First Chicago Trust Company of
New York
Attention: Corporate Actions
525 Washington Blvd.
Jersey City, NJ 07310

     If you have tendered shares in your account in the Retirement 401(k)
Investment Plan of Dime or the North American Mortgage Company Retirement and
401(k) Savings Plan into North Fork's hostile offer, then you should follow the
directions with regard to withdrawing your tendered shares appearing in the
"Letter to Participants in the Retirement 401(k) Investment Plan of Dime
Bancorp, Inc." or the "Letter to Participants in the North American Mortgage
Company Retirement and 401(k) Savings Plan," each as sent separately.

     More information about North Fork's hostile offer is discussed in Section 2
of this document.

     DETERMINATION OF VALIDITY; REJECTION OF SHARES; WAIVER OF DEFECTS; NO
OBLIGATION TO GIVE NOTICE OF DEFECTS.  All questions as to the number of shares
to be accepted, the price to be paid for shares to be accepted and the validity,
form, eligibility (including time of receipt) and acceptance for payment of any
tender of shares will be determined by us, in our sole discretion, and our
determination will be final and binding on all parties. We reserve the absolute
right to reject any or all tenders of any shares that we determine are not in
proper form or the acceptance for payment of or payment for which we determine
may be unlawful. We also reserve the absolute right to waive any of the
conditions of our offer or any defect or irregularity in any tender with respect
to any particular shares or any particular stockholder and our interpretation of
the terms of our offer will be final and binding on all parties. No tender of
shares will be deemed to have been properly made until all defects or
irregularities have been cured by the tendering stockholder or waived by us.
Unless waived, any defects and irregularities in connection with tenders must be
cured within the time period, if any, we determine. Neither we, nor any of the
depositary, the information agent, either dealer manager or any other person
will be under any duty to give notification of any defects or irregularities in
any tender or incur any liability for failure to give any such notification.

     YOUR REPRESENTATION AND WARRANTY; OUR ACCEPTANCE CONSTITUTES AN
AGREEMENT.  A tender of shares under any of the procedures described above will
constitute your acceptance of the terms and conditions of our offer, as well as
your representation and warranty to us that:

     - you have a "net long position" in the shares or equivalent securities at
       least equal to the shares tendered within the meaning of Rule 14e-4
       promulgated by the SEC under the Exchange Act, and

     - the tender of shares complies with Rule 14e-4.

     It is a violation of Rule 14e-4 for a person, directly or indirectly, to
tender shares for that person's own account unless, at the time of tender and at
the end of the proration period or period during which shares are accepted by
lot (including any extensions of any period), the person so tendering

     - has a net long position equal to or greater than the amount tendered in
       the subject securities or securities immediately convertible into, or
       exchangeable or exercisable for, the subject securities, and

     - will deliver or cause to be delivered the shares in accordance with the
       terms of the tender offer.

     Rule 14e-4 provides a similar restriction applicable to the tender or
guarantee of a tender on behalf of another person.

     Our acceptance for payment of shares tendered under our offer will
constitute a binding agreement between you and us upon the terms and conditions
of our offer described in this and related documents.

                                       24
<PAGE>   28

     RETURN OF UNPURCHASED SHARES.  If any tendered shares are not purchased or
are properly withdrawn, or if less than all shares evidenced by a stockholder's
certificates are tendered, certificates for unpurchased shares will be returned
as soon as practicable after the expiration or termination of our offer or the
proper withdrawal of the shares, as applicable. In the case of shares tendered
by book-entry transfer at the book-entry transfer facility, the shares will be
credited to the appropriate account maintained by the tendering stockholder at
the book-entry transfer facility. In each case, shares will be returned or
credited without expense to the stockholder.

     FEDERAL BACKUP WITHHOLDING TAX.  Under the United States federal backup
withholding tax rules, 31% of the gross proceeds payable to a stockholder or
other payee in the tender offer must be withheld and remitted to the United
States Treasury, unless the stockholder or other payee provides such person's
taxpayer identification number (employer identification number or social
security number) to the depositary and certifies under penalties of perjury that
such number is correct or otherwise establishes an exemption. If the depositary
is not provided with the correct taxpayer identification number or another
adequate basis for exemption, the holder may be subject to certain penalties
imposed by the Internal Revenue Service. Therefore, each tendering stockholder
should complete and sign the substitute Form W-9 included as part of the letter
of transmittal in order to provide the information and certification necessary
to avoid backup withholding, unless such stockholder otherwise establishes to
the satisfaction of the depositary that the stockholder is not subject to backup
withholding.

     Certain stockholders (including, among others, all corporations and certain
foreign stockholders (in addition to foreign corporations)) are not subject to
these backup withholding rules. In order for a foreign stockholder to qualify as
an exempt recipient, that stockholder must submit an IRS Form W-8 or a
Substitute Form W-8, signed under penalties of perjury, attesting to that
stockholder's exempt status. The applicable form can be obtained from the
depositary. See Instruction 13 of the letter of transmittal.

     TO PREVENT FEDERAL BACKUP WITHHOLDING TAX EQUAL TO 31% OF THE GROSS
PAYMENTS MADE TO STOCKHOLDERS FOR SHARES PURCHASED UNDER OUR OFFER, EACH
STOCKHOLDER WHO DOES NOT OTHERWISE ESTABLISH AN EXEMPTION FROM SUCH WITHHOLDING
MUST PROVIDE THE DEPOSITARY WITH THE STOCKHOLDER'S CORRECT TAXPAYER
IDENTIFICATION NUMBER AND PROVIDE OTHER INFORMATION BY COMPLETING THE SUBSTITUTE
FORM W-9 INCLUDED WITH THE LETTER OF TRANSMITTAL.

     For a discussion of United States federal income tax consequences to
tendering stockholders, see Section 14.

     LOST OR DESTROYED CERTIFICATES.  If your certificate for part or all of
your shares has been lost, stolen, misplaced or destroyed, you should contact
EquiServe Trust Company, N.A., the transfer agent for our shares, at
800-730-4001 (toll free), for instructions as to obtaining an affidavit of loss.
The affidavit of loss will then be required to be submitted together with the
letter of transmittal in order to receive payment for shares that are tendered
and accepted for payment. A bond may be required to be posted by you to secure
against the risk that the certificates may be subsequently recirculated. You are
urged to contact EquiServe Trust Company, N.A. immediately in order to receive
further instructions, to permit timely processing of this documentation and for
a determination as to whether you will need to post a bond.

SECTION 4.  WITHDRAWAL RIGHTS.

     Shares tendered may be withdrawn at any time before the expiration date
and, unless accepted for payment by us after the expiration date, may also be
withdrawn at any time after 12:00 midnight, New York City time, on Tuesday,
September 26, 2000. Except as otherwise provided in this Section 4, tenders of
shares are irrevocable.

     For a withdrawal to be effective, a written notice of withdrawal must be
timely received by the depositary at its address or facsimile number appearing
on the back page of this document. Any notice of withdrawal must specify the
name of the tendering stockholder, the number of shares to be withdrawn and the
name of the registered holder of the shares. If the certificates for shares to
be withdrawn have been delivered or otherwise identified to the depositary,
then, before the release of such certificates, the serial

                                       25
<PAGE>   29

numbers shown on such certificates must be submitted to the depositary and the
signature(s) on the notice of withdrawal must be guaranteed by an eligible
guarantor institution, unless the shares have been tendered for the account of
an eligible guarantor institution.

     If shares have been tendered under the procedure for book-entry transfer
set forth in Section 3, any notice of withdrawal also must specify the name and
the number of the account at the book-entry transfer facility to be credited
with the withdrawn shares and must otherwise comply with the book-entry transfer
facility's procedures.

     All questions as to the form and validity (including the time of receipt)
of any notice of withdrawal will be determined by us, and our determination will
be final and binding. Neither we, nor any of the depositary, the information
agent, either of the dealer managers or any other person will be under any duty
to give notification of any defects or irregularities in any notice of
withdrawal or incur any liability for failure to give any such notification.

     Participants in either the Retirement 401(k) Investment Plan of Dime or the
North American Mortgage Company Retirement and 401(k) Savings Plan who wish to
withdraw their shares must follow the instructions found in either the "Letter
to Participants in the Retirement 401(k) Investment Plan of Dime Bancorp, Inc."
or the "Letter to Participants in the North American Mortgage Company Retirement
and 401(k) Savings Plan," as applicable, each of which has been sent separately
to participants in these 401(k) savings plans.

     Withdrawals may not be rescinded, and any shares properly withdrawn will
thereafter be deemed not properly tendered for purposes of our offer unless the
withdrawn shares are properly re-tendered before the expiration date by
following one of the procedures described in Section 3.

     If we extend our offer, if we are delayed in our purchase of shares or are
unable to purchase shares under our offer for any reason, then, without
prejudice to our rights under our offer, the depositary may, subject to
applicable law, retain tendered shares on our behalf, and such shares may not be
withdrawn except to the extent tendering stockholders are entitled to withdrawal
rights as described in this Section 4.

SECTION 5.  PURCHASE OF SHARES AND PAYMENT OF PURCHASE PRICE.

     Upon the terms and conditions of our offer, as soon as practicable
following the expiration date, we will:

     - select the purchase price we will pay for shares properly tendered and
       not properly withdrawn, taking into account the number of shares so
       tendered and the prices specified by tendering stockholders, and

     - accept for payment and pay for, and thereby purchase, shares properly
       tendered at prices equal to or below the purchase price we select and not
       properly withdrawn.

     For purposes of our offer, we will be deemed to have accepted for payment
and therefore purchased shares that are properly tendered at or below the
purchase price and not properly withdrawn, subject to the odd lot priority,
conditional tender and proration provisions of our offer, only when, as and if
we give oral or written notice to the depositary of our acceptance of the shares
for payment.

     Upon the terms and conditions of our offer, as soon as practicable after
the expiration date, we will accept for payment and pay a single per share
purchase price for 13,607,664 shares, subject to increase or decrease as
provided in Sections 1 and 15, if properly tendered and not properly withdrawn,
or such lesser number of shares as are properly tendered and not properly
withdrawn, at prices between $16.00 and $18.00 per share.

     We will pay for shares purchased under our offer by depositing the
aggregate purchase price for the shares with the depositary, which will act as
agent for tendering stockholders for the purpose of receiving payment from us
and transmitting payment to the tendering stockholders.

                                       26
<PAGE>   30

     In the event of proration, we will determine the proration percentage and
pay for those tendered shares accepted for payment as soon as practicable after
the expiration date. However, we do not expect to be able to announce the final
results of any proration or to be able to commence payment for shares purchased
until approximately seven to ten business days after the expiration date.

     We will not pay interest on the purchase price regardless of any delay in
making such payment. In addition, if certain events occur, we may not be
obligated to purchase shares in our offer. See the conditions to our offer in
Section 7.

     We will pay all stock transfer taxes, if any, payable on the transfer to us
of shares purchased under our offer. If, however, (a) payment of the purchase
price is to be made to any person other than the registered holder, (b) shares
not tendered or rejected for purchase are to be registered in the name of any
person other than the registered holder, or (c) certificates representing
tendered shares are registered in the name of any person other than the person
signing the letter of transmittal, the amount of all stock transfer taxes, if
any (whether imposed on the registered holder the other person or otherwise),
payable on account of the transfer to the other person, will be deducted from
the purchase price unless satisfactory evidence of the payment of the stock
transfer taxes, or exemption therefrom, is submitted. See Instruction 7 of the
letter of transmittal.

     ANY TENDERING STOCKHOLDER OR OTHER PAYEE WHO FAILS TO COMPLETE FULLY, SIGN
AND RETURN TO THE DEPOSITARY THE SUBSTITUTE FORM W-9 INCLUDED WITH THE LETTER OF
TRANSMITTAL MAY BE SUBJECT TO FEDERAL INCOME BACKUP WITHHOLDING TAX OF 31% OF
THE GROSS PROCEEDS PAID TO THE STOCKHOLDER OR OTHER PAYEE UNDER OUR OFFER. SEE
SECTION 3. ALSO SEE SECTION 14 REGARDING ADDITIONAL UNITED STATES FEDERAL INCOME
TAX CONSEQUENCES.

SECTION 6.  CONDITIONAL TENDER PROCEDURES.

     Under certain circumstances and subject to the exceptions for odd lot
holders described in Section 1, we may prorate the number of shares purchased
pursuant to our offer. As discussed in Section 14, the number of shares to be
purchased from a particular stockholder may affect the tax treatment of the
purchase to the stockholder and the stockholder's decision whether to tender.
The conditional tender alternative is made available so that a stockholder may
seek to structure the purchase of shares pursuant to our offer in such a manner
that the purchase will be treated as a sale of such shares by the stockholder,
rather than the payment of a dividend to the stockholder, for federal income tax
purposes. Accordingly, a stockholder may tender shares subject to the condition
that all or a specified minimum number of the stockholder's shares tendered
pursuant to a letter of transmittal or notice of guaranteed delivery must be
purchased if any of the stockholder's tendered shares are purchased. If you are
an odd lot holder and you tender all of your shares, you cannot conditionally
tender, since your shares will not be subject to proration. EACH STOCKHOLDER IS
URGED TO CONSULT WITH HIS OR HER OWN TAX ADVISOR.

     If you wish to make a conditional tender you must indicate this in the box
captioned "Conditional Tender" in the letter of transmittal or, if applicable,
the notice of guaranteed delivery. In this box in the letter of transmittal or
the notice of guaranteed delivery, you must calculate and appropriately indicate
the minimum number of shares that must be purchased if any are to be purchased.
After our offer expires, if greater than 13,607,664 shares are properly tendered
and not properly withdrawn and we must prorate our acceptance of and payment for
tendered shares, we will calculate a preliminary proration percentage based upon
all shares properly tendered, conditionally or unconditionally. If the effect of
this preliminary proration would be to reduce the number of shares to be
purchased from any stockholder below the minimum number specified by that
stockholder, the conditional tender will automatically be regarded as withdrawn,
unless chosen by lot for reinstatement as discussed in the next paragraph.

     After giving effect to these withdrawals, we will accept the remaining
shares properly tendered, conditionally or unconditionally, on a pro rata basis,
if necessary. If we are able to purchase all of the remaining tendered shares
and the number that we would purchase would be below 13,607,664, then, to the
extent feasible, we will select enough of the conditional tenders that would
otherwise have been deemed withdrawn to permit us to purchase 13,607,664 shares.
In selecting among these conditional

                                       27
<PAGE>   31

tenders, we will select by random lot and will select only from stockholders who
tendered all of their shares. Upon selection by lot, if any, we will limit our
purchase in each case to the designated minimum number of shares to be
purchased.

     All shares tendered by a stockholder subject to a conditional tender
pursuant to the letter of transmittal or notice of guaranteed delivery, regarded
as withdrawn as a result of proration and not eventually purchased will be
returned as soon as practicable after the expiration date without any expense to
the stockholder.

SECTION 7.  CONDITIONS OF OUR OFFER.

     In addition to a variety of general conditions described below, our offer
is conditioned on the satisfaction or, where permissible, waiver of the
conditions to the second closing of the Warburg investment described in Section
2 above. The second closing of the Warburg investment is conditioned on the
following:

     - there has not occurred, since July 6, 2000, any change or development
       with respect to us or any combination of such changes or developments
       which has had or is reasonably likely to have a material adverse affect
       on us;

     - certain representations and warranties made by us to Warburg, including
       representations and warranties concerning our valid organization,
       capitalization, authority to enter into and perform obligations under the
       investment agreement, financial statements and SEC filings, continue to
       be true and correct, and we have performed all of our material
       obligations under the investment agreement;

     - all approvals and authorizations of governmental or self-regulatory
       agencies have been obtained and are in full force and effect (including
       authorization pursuant to the Hart-Scott-Rodino Act and a determination
       by the Office of Thrift Supervision that Warburg does not control us
       pursuant to certain bank regulations), and all waiting periods pursuant
       to such approvals or authorizations have expired; and

     - no provision of any applicable law or regulation and no judgment,
       injunction, order or decree prohibits the second closing.

     Notwithstanding any other provision of our offer, we will not be required
to accept for payment, purchase or pay for any shares tendered, and may
terminate or amend our offer or may postpone the acceptance for payment of, or
the purchase of and the payment for shares tendered, subject to the rules
promulgated by the SEC under the Exchange Act, if:

     (1) at the expiration date, the conditions to the second closing to the
         Warburg investment (described above) have not been satisfied or, where
         permissible, waived;

     (2) at any time on or after August 1, 2000 and before our acceptance for
         payment of properly tendered shares any of the following events have
         occurred (or have been determined by us to have occurred) that, in our
         reasonable judgment makes it inadvisable for us to proceed with our
         offer or with acceptance for payment:

          - there has been threatened, instituted or pending any action or
            proceeding by any government or governmental, regulatory or
            administrative agency, authority or tribunal or any other person,
            domestic or foreign, before any court, authority, agency or tribunal
            that directly or indirectly challenges the making of our offer, the
            acquisition of some or all of the shares under our offer or
            otherwise relates in any manner to our offer, including the other
            conditions to our offer;

          - there has been any action threatened, pending or taken, or approval
            withheld, or any statute, rule, regulation, judgment, order or
            injunction threatened, proposed, sought, promulgated, enacted,
            entered, amended, enforced or deemed to be applicable to our offer
            or to us or any of

                                       28
<PAGE>   32

         our subsidiaries, by any court or any authority, agency or tribunal
         that, in our reasonable judgment, would or might directly or indirectly

         - make the acceptance for payment of, or payment for, some or all of
           the shares illegal or otherwise restrict or prohibit completion of
           our offer, or

         - delay or restrict our ability, or render us unable, to accept for
           payment or pay for some or all of the shares; or

          - there has occurred any of the following:

         - any general suspension of trading in, or limitation on prices for,
           securities on any national securities exchange or in the
           over-the-counter market in the United States,

         - the declaration of a banking moratorium or any suspension of payments
           in respect of banks in the United States,

         - the commencement of a war, armed hostilities or other international
           or national calamity directly or indirectly involving the United
           States or any of its territories,

         - any limitation (whether or not mandatory) by any governmental,
           regulatory or administrative agency or authority on, or any event, or
           any disruption or adverse change in the financial or capital markets
           generally or the market for loan syndications in particular, that, in
           our reasonable judgment, might affect, the extension of credit by
           banks or other lending institutions in the United States,

         - any significant decrease in the market price of our common stock or
           any change in the general political, market, economic or financial
           conditions in the United States or abroad that could, in our
           reasonable judgment, have a material adverse effect on our business,
           operations or prospects or the trading of our common stock,

         - any change or changes in the business, financial condition, assets,
           income, operations, prospects or stock ownership of us or our
           subsidiaries that, in our reasonable judgment, is or may be material
           and adverse to us or our subsidiaries; or

     (3) at any time on or after August 1, 2000 and before the expiration date
         either of the following events have occurred:

          - a tender offer or exchange offer for any or all of our common stock,
            or any merger, business combination or other similar transaction
            with or involving us or any of our subsidiaries, has been proposed,
            announced or made by any person, other than (1) Warburg's
            investment, (2) North Fork's hostile offer (other than a material
            change in the terms or conditions of North Fork's hostile offer) and
            (3) our offer; or

          - North Fork closes, and acquires securities pursuant to, its hostile
            offer.

     The conditions to our offer are for our sole benefit and may be asserted by
us regardless of the circumstances (including any action or inaction by us)
giving rise to any such condition and, where permissible, may be waived by us,
in whole or in part at any time and from time to time in our sole discretion.
Our failure at any time to exercise any of the foregoing rights shall not be
deemed a waiver of any right, and each right shall be deemed an ongoing right
which may be asserted at any time and from time to time. Any determination or
judgment by us concerning the events described above will be final and binding
on all parties.

SECTION 8.  PRICE RANGE OF SHARES; DIVIDENDS; OUR RIGHTS AGREEMENT.

     SHARE PRICES.  Our common stock is listed and traded on the NYSE under the
trading symbol "DME." The following table sets forth, for the fiscal quarters
indicated, the intraday high and low sales

                                       29
<PAGE>   33

prices per share on the NYSE Composite Tape and the cash dividends declared per
share of our common stock.

<TABLE>
<CAPTION>
                                                              HIGH           LOW            DIVIDEND
                                                              ----           ----           --------
<S>                                                           <C>            <C>            <C>
1998:
  First Quarter.............................................  $ 31 1/4       $ 23            $0.04
  Second Quarter............................................    32 1/2         27 5/8         0.05
  Third Quarter.............................................    33 1/16        18 1/4         0.05
  Fourth Quarter............................................    28             17 1/8         0.05
1999:
  First Quarter.............................................    27 3/16        22             0.05
  Second Quarter............................................    25 1/8         19 13/16       0.06
  Third Quarter.............................................    21 13/16       16 1/4         0.06
  Fourth Quarter............................................    19 11/16       14 3/4         0.06
2000:
  First Quarter.............................................    18 1/2         11 5/16        0.06
  Second Quarter............................................    19 9/16        15 3/4         0.08
  Third Quarter (through July 28, 2000).....................    17 1/8         15             0.08
</TABLE>

     On July 28, 2000, a date close to the date of this document, the closing
price of our common stock on the NYSE Composite Tape was $16 3/16. WE URGE YOU
TO OBTAIN MORE CURRENT MARKET QUOTATIONS FOR OUR COMMON STOCK.

     RIGHTS AGREEMENT.  Each share of Dime common stock has attached to it one
right issued pursuant to a stockholder protection rights agreement, dated
October 20, 1995, between Dime and the First National Bank of Boston, as rights
agent. As of June 23, 2000, the rights agent has been changed to The Dime
Savings Bank of New York, FSB.

     Each right entitles its holder to purchase one-hundredth of a share of
participating preferred stock of Dime at an exercise price of $50, subject to
adjustment, after the separation time, which is after the close of business on
the earlier of:

     - the tenth business day after commencement of a tender or exchange offer
       that, if consummated, would result in a person becoming an acquiring
       person, which is defined in the rights agreement as a person beneficially
       owning 20% or more of the outstanding shares of Dime common stock and

     - the tenth business day after the first date of public announcement that a
       person has become an acquiring person, which is also called the flip-in
       date.

Your board has acted to delay the separation time pursuant to provisions of the
rights agreement that would have otherwise occurred upon announcement of North
Fork's hostile offer.

     The rights will not be exercisable until the business day following the
separation time. The rights will expire on the earlier of:

     - the close of business on November 6, 2005,

     - redemption, as described below,

     - an exchange for common stock, as described below, or

     - the merger of Dime into another corporation pursuant to an agreement
       entered into prior to a flip-in date.

Your board of directors may, at any time prior to occurrence of a flip-in date,
redeem all the rights at a price of $0.01 per right.

                                       30
<PAGE>   34

     If a flip-in date occurs, each right, other than those held by the
acquiring person or any affiliate or associate of the acquiring person or by any
transferees of any of these persons, will constitute the right to purchase
shares of Dime common stock having an aggregate market price equal to $100 in
cash, subject to adjustment. In addition, your board of directors may at any
time between a flip-in date and the time that an acquiring person becomes the
beneficial owner of more than 50% of the outstanding shares of Dime common stock
elect to exchange the rights for shares of Dime common stock at an exchange
ratio of one share of Dime common stock per right.

     Under the rights agreement, we may not consolidate or merge, or engage in
other similar transactions, with an acquiring person without entering into a
supplemental agreement with the acquiring person providing that, upon
consummation or occurrence of the transaction, each right shall thereafter
constitute the right to purchase common stock of the acquiring person having an
aggregate market price equal to $100 in cash, subject to adjustment.

     On July 6, 2000, three amendments to the rights agreement were made by the
board of directors. These amendments are discussed in the "Amendments to
Stockholder Protection Rights Agreement" paragraph of Section 2.

     The rights will not prevent a takeover of Dime. The rights, however, may
have antitakeover effects. The rights may cause substantial dilution to a person
or group that acquires 20% or more of the outstanding Dime common stock unless
the rights are first redeemed by your board of directors.

     A description of the rights agreement specifying the terms of the rights
has been included in reports filed by us with the SEC. The description above
does not purport to be a complete description and it is qualified in all
respects by reference to the rights agreement included in Dime's Form 8-A filed
with the SEC on November 3, 1995, as the Form 8-A was amended on June 23, 2000
and July 12, 2000. This Form 8-A, as amended, is incorporated by reference into
this document.

SECTION 9.  SOURCE AND AMOUNT OF FUNDS.

     Assuming that 13,607,664 shares are tendered in the offer at a price
between $16.00 and $18.00 per share, the aggregate purchase price paid by us
will be between $217,722,624 and $244,937,952. We expect that our fees and
expenses for the offer will be about $1,400,000.

     We anticipate that we will have all of the funds necessary to purchase
shares tendered in our offer, as well as to pay related fees and expenses, from
the Warburg investment and available cash.

     Our offer is not contingent on financing and we do not anticipate the need
for any additional financing, including loans or other credit arrangements, to
consummate our offer.

SECTION 10.  INFORMATION ABOUT US.

     GENERAL.  We are a Delaware corporation and a savings and loan holding
company. We are the parent holding company for Dime Savings Bank, a federally
chartered savings bank currently servicing consumers and businesses through 127
branches located throughout the greater New York City metropolitan area. Through
Dime Savings Bank and its subsidiaries, including North American Mortgage
Company, we provide consumer loans, insurance products and mortgage banking
services throughout the United States. At December 31, 1999, we had consolidated
assets of $23.9 billion, consolidated deposits of $14.3 billion and consolidated
stockholders' equity of $1.5 billion. At June 30, 2000, we had consolidated
assets of $25.3 billion, consolidated deposits of $14.3 billion and consolidated
stockholders' equity of $1.6 billion.

     Our headquarters are located at 589 Fifth Avenue, New York, New York 10017.
Our telephone number is (212) 326-6170.

     ADDITIONAL INFORMATION.  We are subject to the information and reporting
requirements of the Exchange Act, and in accordance with such laws we file with
the SEC periodic reports, proxy statements and other information relating to our
business, financial condition and other matters. We are required to disclose in
these proxy statements filed with the SEC certain information, as of particular
dates,

                                       31
<PAGE>   35

concerning our directors and executive officers, their compensation, stock
options granted to them, the principal holders of our securities and any
material interest of such persons in transactions with us. We have also filed
with the SEC an Issuer Tender Offer Statement on Schedule TO, which includes
additional information with respect to our offer.

     The reports, statements and other information (including any exhibits,
amendments or supplements to such documents) we file may be inspected and copied
at the public reference facilities maintained by the SEC at Room 1024, 450 Fifth
Street, N.W., Washington, D.C. 20549; and at the following regional offices of
the SEC: 7 World Trade Center, Suite 1300, New York, New York 10048; and
Citicorp Center, 500 West Madison Street, Suite 1400, Chicago, Illinois 60661.
Copies of this material can also be obtained by mail, upon payment of the SEC's
customary charges, by writing to the Public Reference Section at 450 Fifth
Street, N.W., Washington, D.C. 20549. The SEC also maintains a web site on the
Internet at http://www.sec.gov that contains reports, proxy and information
statements and other information regarding registrants that file electronically
with the SEC. These reports, statements and other information concerning us can
also be inspected at the offices of the New York Stock Exchange, 20 Broad
Street, New York, New York 10005.

     INCORPORATION BY REFERENCE.  The rules of the SEC allow us to "incorporate
by reference" information into this document, which means that we can disclose
important information to you by referring you to another document filed
separately with the SEC. These documents contain important information about us.

<TABLE>
<CAPTION>
SEC FILINGS (FILE NO. 001-13094)                            PERIOD OR DATE FILED
--------------------------------                            --------------------
<S>                                             <C>
Annual Report on Form 10-K..................    Year ended December 31, 1999, as amended by
                                                Form 10-K/A filed on March 31, 2000
Quarterly Reports on Form 10-Q..............    Quarter ended March 31, 2000
Current Reports on Form 8-K.................    Reports filed January 20, 2000, February 29,
                                                2000, March 8, 2000 (2 reports filed on
                                                March 8, 2000), March 10, 2000, March 13,
                                                2000 (2 reports filed on March 13, 2000),
                                                March 14, 2000, March 21, 2000, April 19,
                                                2000, April 28, 2000, May 1, 2000, July 11,
                                                2000, and July 12, 2000
Proxy Statement for 2000 Annual
Stockholders Meeting........................    Filed June 12, 2000
Solicitation/Recommendation Statement on
Schedule 14D-9..............................    Filed March 21, 2000, as amended through
                                                Amendment No. 23, dated July 28, 2000
Form 8-A....................................    Filed November 3, 1995, as amended June 23,
                                                2000 and July 12, 2000
</TABLE>

     We incorporate these documents and any additional documents that we may
file with the SEC between the date of this document and the date of expiration
of withdrawal rights by reference. Those documents include periodic reports,
such as annual reports on Form 10-K, quarterly reports on Form 10-Q and current
reports on Form 8-K, as well as proxy statements.

     The documents incorporated by reference, including particularly our Annual
Report on Form 10-K for the year ended December 31, 1999, as amended, and our
Quarterly Reports on Form 10-Q filed since the 1999 Form 10-K, contain financial
statements and other information about our financial condition that is being
incorporated by reference into this document.

     You can obtain any of the documents incorporated by reference in this
document from us without charge, excluding any exhibits to those documents, by
requesting them in writing or by telephone from us at Investor Relations
Department, 589 Fifth Avenue, New York, New York, 10017, telephone: (212) 326-
6170. Please be sure to include your complete name and address in your request.
If you request any incorporated documents, we will mail them to you by first
class mail, or another equally prompt means,

                                       32
<PAGE>   36

within one business day after we receive your request. In addition, you can
obtain copies of these documents from the SEC's website. Such documents may also
be inspected at the locations described above.

SECTION 11.  INFORMATION ABOUT OUR SHARES; INTEREST OF DIRECTORS AND EXECUTIVE
             OFFICERS; TRANSACTIONS AND ARRANGEMENTS CONCERNING SHARES.

     SHARES OUTSTANDING.  As of July 6, 2000, the day we announced our offer, we
had 109,298,503 issued and outstanding shares of common stock and held
10,953,956 shares in treasury. On July 6, 2000, Warburg purchased rights to
acquire 12,009.491 shares of Series B stock of Dime. Assuming that the second
closing of the Warburg investment occurs, Warburg will purchase an additional
1,598.173 shares of Series B stock and will own a total of 13,607.664 shares of
Series B stock. See the description of the Warburg investment in Section 2.
Because the total Warburg ownership of Series B stock represents the equivalent
of 13,607,664 shares of our common stock, after the total Warburg investment is
completed we will have approximately 122,906,167 shares of common stock and its
equivalents issued and outstanding.

     The 13,607,664 shares that we are offering to purchase represent (1)
approximately 12.45% of our issued and outstanding stock as of July 6, 2000 and
(2) approximately 11.07% of the common stock and its equivalents to be issued
and outstanding after completion of the Warburg investment and the issuance of
all of the Series B stock to Warburg. The 13,607,664 shares that we are offering
to purchase also represent the number of shares (or their equivalent in
preferred stock) that we anticipate issuing to Warburg upon completion of their
investment in Dime (before exercise of the warrants we have granted them).
Therefore, after completion of the Warburg investment and after completion of
our offer, if we are able to purchase 13,607,664 shares, we anticipate that the
number of issued and outstanding shares of our common stock (and its
equivalents) will remain the same as on July 6, 2000 before Warburg's
investment.

     INTEREST OF DIRECTORS AND EXECUTIVE OFFICERS.  Our proxy statement for our
2000 annual stockholders meeting contains information about our directors and
executive officers, including information relating to stock ownership,
agreements concerning our securities (including option and restricted stock
grants) and the business address of such directors and officers. This proxy
statement is incorporated by reference into this document. As of May 18, 2000,
the date as of which this information was presented in our proxy statement, the
number of shares of our common stock issued and outstanding was 111,724,928. Our
directors and executive officers as a group (24 persons) owned an aggregate of
3,525,684 shares of our common stock, representing approximately 3.16% of our
issued and outstanding stock as of that date. No director or executive officer
owned more than 1% of the shares of our common stock as of that date.

     As of July 28, 2000, taking into account the effect of

     - a purchase of 2,469,100 shares from Hudson United Bancorp on June 2, 2000
       (as discussed below),

     - the issuance of an equivalent of 12,009,491 shares of common stock to
       Warburg as a result of its investment in us on July 6, 2000,

     - a grant to Mr. Terracciano of the right to purchase 200,000 shares of
       restricted stock between July 6, 2000 and September 4, 2000, and

     - the retirement of Dr. Paul A. Qualben from our board of directors
       effective on July 14, 2000 (Dr. Qualben owned 30,506 shares of our common
       stock at that date)

there were the equivalent of 121,307,994 shares of our common stock issued and
outstanding. Our directors and officers as a group (24 persons) beneficially
owned 3,695,178 shares, or 3.05%, of our common stock at that date.

     Upon completion of the Warburg investment (including the issuance of the
equivalent of an additional 1,598,173 shares of our common stock to Warburg) and
upon completion of our offer, we anticipate that there will be 109,298,503
shares of our common stock issued and outstanding. Assuming no changes in the
beneficial ownership of our directors and officers, as a group they will
beneficially own 3.38% of our common stock at that time.

                                       33
<PAGE>   37

     Our directors and executive officers are entitled to participate in our
offer on the same basis as all other stockholders. However, all of our directors
and executive officers have informed us that they do not intend to tender any
shares into our offer.

     INFORMATION REGARDING NEW DIRECTORS.  Information relating to stock
ownership and agreements concerning our securities presented in our 2000 annual
meeting proxy statement, which is incorporated by reference into this document,
does not include information relating to directors appointed to our board of
directors since the date of the proxy statement.

     Mr. Terracciano.  As discussed in Section 2, Mr. Terracciano was appointed
Chairman of our board of directors, effective July 6, 2000. Mr. Terracciano's
business address is c/o Dime Bancorp, Inc., 589 Fifth Avenue, New York, New York
10017.

     Effective July 6, 2000, we entered into an employment agreement with Mr.
Terracciano. Under this agreement, Mr. Terracciano will serve for three years as
a director and chairman of Dime and will be responsible, in collaboration with
Mr. Toal, for determining and executing our strategy. During the period of his
employment, Mr. Terracciano is to receive an annual salary of at least $600,000
and will be entitled to certain perquisites, including a car and driver. In
addition, pursuant to his agreement, Mr. Terracciano was awarded nonqualified
options to purchase 500,000 shares of Dime common stock at a purchase price of
$17 1/16 per share (the market price of our common stock on July 6, 2000), and
was awarded the right to purchase 200,000 shares of restricted stock at a
purchase price of $.01 per share. The options, which have a fixed term of eleven
years, will vest, and restrictions on the restricted stock will lapse, in equal
installments on the first, second and third anniversaries of their grant date if
Mr. Terracciano remains employed by Dime, subject to earlier vesting or lapse if
Mr. Terracciano dies or becomes disabled during the term of his agreement, or
otherwise in accordance with the terms of the stock incentive plan under which
the options and restricted stock were granted.

     If Mr. Terracciano's employment is involuntarily terminated, other than for
cause, or if Mr. Terracciano terminates his employment following a diminution of
his position, authority, duties or responsibilities, or other breaches by Dime
of his agreement, he will be entitled to a lump sum payment equal to his base
salary for the then-remaining term of his agreement, and all then-unvested
options will vest and the restrictions on restricted stock will lapse. Also, his
agreement provides that if any payment by Dime to Mr. Terracciano would be
subject to an excise tax under section 4999 of the Internal Revenue Code, Dime
will make an additional payment or payments so as to provide Mr. Terracciano
with the amounts he would have received in the absence of the excise tax (and
any related interest and penalties), with a limited exception. The agreement
between us and Mr. Terracciano has been filed as an exhibit to the Schedule TO
filed by us with the SEC regarding our offer and is incorporated into this
document by reference.

     As of the date of this document, as a result of SEC restrictions, Mr.
Terracciano does not own any shares of Dime common stock. However, as discussed
above, between now and September 4, 2000, Mr. Terracciano has the right to
acquire 200,000 shares of restricted Dime common stock.

     Mr. Newman.  Mr. Howard H. Newman is the nominee of Warburg to our board of
directors and we have agreed to appoint Mr. Newman as a director effective upon
antitrust clearance pursuant to the Hart-Scott-Rodino Act for Warburg's
investment. Mr. Newman's business address is c/o E.M. Warburg, Pincus & Co.,
LLC, 466 Lexington Avenue, New York, New York 10017. Mr. Newman does not
currently own any shares of Dime common stock.

     TRANSACTIONS AND ARRANGEMENTS CONCERNING SHARES.  Based on our records and
information provided to us by our directors, executive officers, associates and
subsidiaries, neither we, nor any of our associates or subsidiaries, nor, to the
best of our knowledge, any of our directors or executive officers or any
associates or subsidiaries thereof, have effected any transactions in our shares
during the 60 days before August 1, 2000, except as stated below:

     - On June 2, 2000, we purchased 2,469,100 shares of Dime common stock from
       Hudson United Bancorp at a price of $18 1/4 per share, the closing market
       price for Dime common stock on May 26, 2000. We purchased these shares
       pursuant to the terms of a Termination, Option Cancellation and

                                       34
<PAGE>   38

       Settlement Agreement between us and Hudson, dated April 28, 2000, which
       was filed by Dime on a Form 8-K dated May 1, 2000. The Termination
       Agreement provided that if Hudson wanted to sell its shares of Dime
       common stock, it was required to offer the shares to us before soliciting
       others. The purchase from Hudson was effected as a private purchase of
       the shares.

     - On July 6, 2000, we entered into the employment agreement with Mr.
       Terracciano described above and that agreement contains a grant of
       options to purchase 500,000 shares of our common stock at $17 1/16 per
       share and an award of rights to purchase 200,000 shares of restricted
       common stock at $.01 per share.

     - In the morning before our July 14, 2000 stockholder meeting, consistent
       with advice he obtained from counsel, Mr. Terracciano purchased 30,000
       shares of our common stock on the open market through a broker to show
       his confidence in our plans and initiatives. When we informed him that
       his purchase in fact could have resulted in a technical violation of the
       SEC's tender offer rules, Mr. Terracciano immediately sold the shares
       through a broker on the open market to avoid any appearance of
       impropriety. The purchase price was $16.00 and the price in the sale,
       which occurred on July 24, 2000, was $16 1/16. After paying customary
       brokerage fees, Mr. Terracciano realized a loss on the sale. We
       immediately informed the SEC of the circumstances surrounding the
       purchase and sale.

     - Customary and ongoing purchases of shares through reinvestment of
       dividends under our dividend reinvestment program and purchases under the
       401(k) savings plans. We expect that these plans will, in accordance with
       their terms, elections in effect and present patterns of contribution,
       continue to purchase shares prior to the expiration of our offer.

     Except as otherwise described in this document, and except for customary
margin accounts maintained at a broker by some of our directors and executive
officers, neither we nor, to the best of our knowledge, any of our affiliates,
directors or executive officers, is a party to any agreement, arrangement or
understanding with any other person relating, directly or indirectly, to the
tender offer or with respect to any of our securities, including, but not
limited to, any agreement, arrangement or understanding concerning the transfer
or the voting of our securities, joint ventures, loan or option arrangements,
puts or calls, guarantees of loans, guarantees against loss or the giving or
withholding of proxies, consents or authorizations.

SECTION 12.  EFFECTS OF OUR OFFER ON THE MARKET FOR SHARES; REGISTRATION UNDER
THE EXCHANGE ACT.

     Our purchase of shares in our offer will reduce the number of shares that
might otherwise be traded publicly and may reduce the number of stockholders.
Nonetheless, we anticipate that there will be a sufficient number of shares
outstanding and publicly traded following completion of our offer to ensure a
continued trading market for our shares. Based upon published guidelines of the
NYSE, we do not believe that our purchase of shares under our offer will cause
the remaining outstanding shares of our common stock to be delisted from the
NYSE.

     Our shares are now "margin securities" under the rules of the Federal
Reserve Board. This has the effect, among other things, of allowing brokers to
extend credit to their customers using such shares as collateral. We believe
that, following the purchase of shares under our offer, our shares will continue
to be "margin securities" for purposes of the Federal Reserve Board's margin
rules and regulations.

     Our shares are registered under the Exchange Act, which requires, among
other things, that we furnish certain information to our stockholders and the
SEC and comply with the SEC's proxy rules in connection with meetings of our
stockholders. We believe that our purchase of shares in connection with our
offer will not result in the shares becoming eligible for deregistration under
the Exchange Act.

SECTION 13.  LEGAL MATTERS; REGULATORY APPROVALS.

     Except as otherwise described in this document, we are not aware of any
license or regulatory permit material to our business that would be adversely
affected by our acquisition of shares as contemplated by our offer or of any
approval or other action by any government or governmental, administrative or
regulatory authority or agency, domestic, foreign or supranational, that would
be required for our

                                       35
<PAGE>   39

acquisition or ownership of shares as contemplated by our offer. Should any such
approval or other action be required, we presently contemplate that we will seek
that approval or other action. We are unable to predict whether we will be
required to delay the acceptance for payment of or payment for shares tendered
in response to our offer pending the outcome of any such matter. There can be no
assurance that any such approval or other action, if needed, would be obtained
or would be obtained without substantial cost or conditions or that the failure
to obtain the approval or other action might not result in adverse consequences
to our business and financial condition.

     Our obligation to accept for payment and pay for shares under our offer is
subject to conditions. See Section 7. As discussed in Section 7, our obligation
to close our offer is subject to the satisfaction or waiver of the conditions to
the second closing of the Warburg investment. The second closing of the Warburg
investment is conditioned upon several events, including the receipt of all
necessary government approvals. These government approvals include filings and
expiration of the waiting period under the Hart-Scott-Rodino Act and a
determination by the Office of Thrift Supervision that Warburg does not control
us for purposes of the Home Owners' Loan Act.

SECTION 14.  UNITED STATES FEDERAL INCOME TAX CONSEQUENCES.

     The following summary describes the material United States federal income
tax consequences relating to our offer. This summary is based upon the Internal
Revenue Code of 1986, as amended, Treasury regulations under the Internal
Revenue Code, administrative pronouncements and judicial decisions, all as in
effect as of the date hereof and all of which are subject to change, possibly
with retroactive effect. This summary addresses only stockholders who hold
shares as capital assets within the meaning of Section 1221 of the Internal
Revenue Code and does not address all of the tax consequences that may be
relevant to stockholders in light of their particular circumstances or to
certain types of stockholders subject to special treatment under the Internal
Revenue Code, including, without limitation, certain financial institutions,
dealers in securities or commodities, traders in securities who elect to apply a
mark-to-market method of accounting, insurance companies, tax-exempt
organizations, persons who hold shares as a position in a "straddle" or as a
part of a "hedging," "conversion" or "constructive sale" transaction for United
States federal income tax purposes or persons who received their shares through
the exercise of employee stock options or otherwise as compensation. In
addition, this discussion applies only to "United States holders" (as defined
below). This summary also does not address the state, local or foreign tax
consequences of participating in our offer. For purposes of this discussion, a
"United States holder" means:

     - a citizen or resident of the United States;

     - a corporation or other entity taxable as a corporation created or
       organized in the United States or under the laws of the United States or
       of any political subdivision of the United States;

     - an estate, the income of which is includible in gross income for United
       States federal income tax purposes regardless of its source; or

     - a trust whose administration is subject to the primary supervision of a
       United States court and which has one or more United States persons who
       have the authority to control all of its substantial decisions.

     HOLDERS OF SHARES WHO ARE NOT UNITED STATES HOLDERS SHOULD CONSULT THEIR
TAX ADVISORS REGARDING THE UNITED STATES FEDERAL INCOME TAX CONSEQUENCES AND ANY
APPLICABLE FOREIGN TAX CONSEQUENCES OF OUR OFFER.

     STOCKHOLDERS ARE URGED TO CONSULT THEIR TAX ADVISOR TO DETERMINE THE
PARTICULAR TAX CONSEQUENCES TO THEM OF PARTICIPATING OR NOT PARTICIPATING IN OUR
OFFER.

     CHARACTERIZATION OF THE PURCHASE.  The purchase of a United States holder's
shares by us in our offer will be a taxable transaction for United States
federal income tax purposes. As a consequence of the purchase, a United States
holder will, depending on the United States holder's particular circumstances,
be treated either as having sold the United States holder's shares or as having
received a distribution in respect of stock from Dime.

                                       36
<PAGE>   40

     Under Section 302 of the Internal Revenue Code, a United States holder
whose shares are purchased by us under our offer will be treated as having sold
its shares, and thus will recognize capital gain or loss if the purchase:

     - results in a "complete termination" of the United States holder's equity
       interest in Dime;

     - results in a "substantially disproportionate" redemption with respect to
       the United States holder; or

     - is "not essentially equivalent to a dividend" with respect to the United
       States holder.

     Each of these tests, referred to as the "Section 302 tests," is explained
in more detail below.

     If a United States holder satisfies any of the Section 302 tests explained
below, the United States holder will be treated as if it sold its shares to us
and will recognize capital gain or loss equal to the difference between the
amount of cash received under our offer and the United States holder's adjusted
tax basis in the shares surrendered in exchange therefor. This gain or loss will
be long-term capital gain or loss if the United States holder's holding period
for the shares that were sold exceeds one year as of the date of purchase by us
under our offer. Specified limitations apply to the deductibility of capital
losses by United States holders. Gain or loss must be determined separately for
each block of shares (shares acquired at the same cost in a single transaction)
that is purchased by us from a United States holder under our offer. A United
States holder may be able to designate, generally through its broker, which
blocks of shares it wishes to tender under our offer if less than all of its
shares are tendered under our offer, and the order in which different blocks
will be purchased by Dime in the event of proration under our offer. United
States holders should consult their tax advisors concerning the mechanics and
desirability of that designation.

     If a United States holder does not satisfy any of the Section 302 tests
explained below, the purchase of a United States holder's shares by us under our
offer will not be treated as a sale or exchange under Section 302 of the
Internal Revenue Code with respect to the United States holder. Instead, the
entire amount received by a United States holder with respect to the purchase of
its shares by us under our offer will be treated as a dividend distribution to
the United States holder with respect to its shares under Section 301 of the
Internal Revenue Code, taxable at ordinary income tax rates, to the extent of
the United States holder's share of our current and accumulated earnings and
profits (within the meaning of the Internal Revenue Code). To the extent the
amount exceeds the United States holder's share of our current and accumulated
earnings and profits, the excess first will be treated as a tax-free return of
capital to the extent of the United States holder's adjusted tax basis in its
shares and any remainder will be treated as capital gain (which may be long-term
capital gain as described above). To the extent that a purchase of a United
States holder's shares by us under our offer is treated as the receipt by the
United States holder of a dividend, the United States holder's adjusted tax
basis in the purchased shares will be added to any shares retained by the United
States holder.

     We cannot predict whether or the extent to which our offer will be
oversubscribed. If our offer is oversubscribed, proration of tendered shares
under our offer will cause us to accept fewer shares than are tendered.
Therefore, no assurance can be given that we will purchase a sufficient number
of a United States holder's shares under our offer to ensure that the United
States holder receives sale treatment, rather than dividend treatment, for
United States federal income tax purposes under the rules discussed below.

     CONSTRUCTIVE OWNERSHIP OF STOCK AND OTHER ISSUES.  In applying each of the
Section 302 tests explained below, United States holders must take into account
not only shares that they actually own but also shares they are treated as
owning under the constructive ownership rules of Section 318 of the Internal
Revenue Code. Under the constructive ownership rules, a United States holder is
treated as owning any shares that are owned (actually and in some cases
constructively) by certain related individuals and entities as well as shares
that the United States holder has the right to acquire by exercise of an option
or by conversion or exchange of a security. Due to the factual nature of the
Section 302 tests explained below, United States holders should consult their
tax advisors to determine whether the purchase of their shares under our offer
qualifies for sale treatment in their particular circumstances.

                                       37
<PAGE>   41

     SECTION 302 TESTS.  One of the following tests must be satisfied in order
for the purchase of shares by us under our offer to be treated as a sale or
exchange for federal income tax purposes:

     - Complete Termination Test.  The purchase of a United States holder's
       shares by Dime under our offer will result in a "complete termination" of
       the United States holder's equity interest in Dime if all of the shares
       that are actually owned by the United States holder are sold under our
       offer and all of the shares that are constructively owned by the United
       States holder, if any, are sold under our offer or, with respect to
       shares owned by certain related individuals, the United States holder
       effectively waives, in accordance with Section 302(c) of the Internal
       Revenue Code, attribution of shares which otherwise would be considered
       as constructively owned by the United States holder. United States
       holders wishing to satisfy the "complete termination" test through waiver
       of the constructive ownership rules should consult their tax advisors.

     - Substantially Disproportionate Test.  The purchase of a United States
       holder's shares by us under our offer will result in a "substantially
       disproportionate" redemption with respect to the United States holder if,
       among other things, the percentage of the then outstanding shares
       actually and constructively owned by the United States holder immediately
       after the purchase is less than 80% of the percentage of the shares
       actually and constructively owned by the United States holder immediately
       before the purchase (treating as outstanding all shares purchased under
       our offer).

     - Not Essentially Equivalent to a Dividend Test.  The purchase of a United
       States holder's shares by us under our offer will be treated as "not
       essentially equivalent to a dividend" if the reduction in the United
       States holder's proportionate interest in Dime as a result of the
       purchase constitutes a "meaningful reduction" given the United States
       holder's particular circumstances. Whether the receipt of cash by a
       stockholder who sells shares under our offer will be "not essentially
       equivalent to a dividend" will depend upon the stockholder's particular
       facts and circumstances. The IRS has indicated in a published revenue
       ruling that even a small reduction in the percentage interest of a
       stockholder whose relative stock interest in a publicly held corporation
       is minimal (for example, an interest of less than 1%) and who exercises
       no control over corporate affairs should constitute a "meaningful
       reduction." United States holders should consult their tax advisors as to
       the application of this test in their particular circumstances.

     CORPORATE STOCKHOLDER DIVIDEND TREATMENT.  In the case of a corporate
United States holder, to the extent that any amounts received under our offer
are treated as a dividend, such holder may be eligible for the
dividends-received deduction. The dividends-received deduction is subject to
certain limitations. In addition, any amount received by a corporate United
States holder pursuant to our offer that is treated as a dividend may constitute
an "extraordinary dividend" under Section 1059 of the Internal Revenue Code.
Corporate United States holders should consult their own tax advisors as to the
application of Section 1059 of the Internal Revenue Code to our offer, and to
the tax consequences of dividend treatment in their particular circumstances.

     STOCKHOLDERS WHO DO NOT RECEIVE CASH UNDER OUR OFFER.  Stockholders whose
shares are not purchased by us under our offer will not incur any tax liability
as a result of the completion of our offer.

     BACKUP WITHHOLDING TAX.  See Section 3 with respect to the application of
United States federal backup withholding tax.

     THE DISCUSSION SET FORTH ABOVE IS INCLUDED FOR GENERAL INFORMATION ONLY. WE
URGE YOU TO CONSULT YOUR TAX ADVISOR TO DETERMINE THE PARTICULAR TAX
CONSEQUENCES TO YOU OF OUR OFFER, INCLUDING THE APPLICABILITY AND EFFECT OF
STATE, LOCAL AND FOREIGN TAX LAWS.

SECTION 15.  EXTENSION OF OUR OFFER; TERMINATION; AMENDMENT.

     We reserve the right, in our sole discretion, at any time and from time to
time, to extend the period of time during which our offer is open and to delay
acceptance for payment of, and payment for, any shares by giving oral or written
notice of such extension to the depositary and making a public announcement of
such extension. Our reservation of the right to delay acceptance for payment is
limited

                                       38
<PAGE>   42

by Rule 13e-4(f)(5) promulgated under the Exchange Act, which requires that we
must pay the consideration offered or return the shares tendered promptly after
termination or withdrawal of our offer.

     We also reserve the right, in our sole discretion, to terminate our offer
and not accept for payment or pay for any shares not previously accepted for
payment or paid for or, subject to applicable law, to postpone payment for
shares if any conditions to our offer fail to be satisfied by giving oral or
written notice of such termination or postponement to the depositary and making
a public announcement of such termination or postponement. Our reservation of
the right to delay payment for shares which we have accepted for purchase is
limited by Rule 13e-4(f)(5) promulgated under the Exchange Act, which requires
that we must pay the consideration offered or return the shares tendered
promptly after termination or withdrawal of our offer.

     Subject to compliance with applicable law, we further reserve the right, in
our sole discretion, and regardless of whether or not any of the events or
conditions described in Section 7 have occurred or are deemed by us to have
occurred, to amend our offer in any respect, including, without limitation, by
decreasing or increasing the consideration offered in our offer to holders of
shares or by decreasing or increasing the number of shares being sought in our
offer. Amendments to our offer may be made at any time and from time to time by
public announcement, such announcement, in the case of an extension, to be
issued no later than 9:00 a.m., New York City time, on the next business day
after the last previously scheduled or announced expiration date.

     Without limiting the manner in which we may choose to make a public
announcement, except as required by applicable law, we have no obligation to
publish, advertise or otherwise communicate any such public announcement other
than by making a release through Business Wire, Dow Jones News Service or
another comparable news service.

     If we materially change the terms of our offer or the information
concerning our offer, we will extend our offer to the extent required by Rules
13e-4(d)(2), 13e-4(e)(3) and 13e-4(f)(1) promulgated under the Exchange Act.
These rules and certain related releases and interpretations of the SEC provide
that the minimum period during which a tender offer must remain open following
material changes in the terms of the tender offer or information concerning the
tender offer (other than a change in price or a change in percentage of
securities sought) will depend on the facts and circumstances, including the
relative materiality of such terms or information. If

     - we undertake any of the following actions:

      - increase or decrease the range of prices to be paid for the shares,

      - increase the number of shares being sought in our offer by more than 2%
        of our outstanding common stock,

      - decrease the number of shares being sought in our offer, or

      - materially change the fees to be paid to our dealer managers, and

     - our offer is scheduled to expire at any time earlier than the expiration
       of a period ending on the tenth business day from, and including, the
       date that such notice of an increase or decrease is first published, sent
       or given to security holders in the manner specified in this Section 15,

then our offer will be extended until the expiration of such period of ten
business days.

SECTION 16.  FEES AND EXPENSES.

     We have retained Credit Suisse First Boston and Merrill Lynch to act as our
financial advisors and as the dealer managers in connection with our offer. In
this role, Credit Suisse First Boston and Merrill Lynch may contact brokers,
dealers and similar entities and may provide information regarding our offer to
those that they contact or persons that contact them. Each of Credit Suisse
First Boston and Merrill Lynch will receive reasonable and customary
compensation in connection with our offer. We have also agreed to reimburse each
of Credit Suisse First Boston and Merrill Lynch for reasonable out-of-pocket
expenses incurred in connection with our offer, including reasonable fees and
expenses of counsel, and to indemnify each of Credit Suisse First Boston and
Merrill Lynch against certain liabilities in connection

                                       39
<PAGE>   43

with our offer, including liabilities under the federal securities laws. Each of
Credit Suisse First Boston and Merrill Lynch has rendered various investment
banking and other services to us in the past and may continue to render such
services, for which they have received and may continue to receive customary
compensation from us. In the ordinary course of its trading and brokerage
activities, each of Credit Suisse First Boston and Merrill Lynch and their
affiliates may hold positions, for their own accounts or for those of their
customers, in our securities.

     Credit Suisse First Boston and Merrill Lynch are also acting as our
financial advisors in connection with North Fork's hostile offer and the Warburg
investment. The material terms of their agreements with us have been described
in the section entitled "Information Concerning Participants -- Other Persons"
in Annex A to our proxy statement for the 2000 annual stockholders meeting and
in our Schedule 14D-9 filed in connection with North Fork's hostile offer. As
described in these documents, additional market-rate fees for advisory services
not covered by the agreements were to be paid to Credit Suisse First Boston and
Merrill Lynch for subsequent transactions, such as a placement fee in connection
with Warburg's investment. Final compensation to these advisors for the Warburg
investment has not yet been agreed to, but it will include provisions for
reimbursement and indemnification as in their original agreements with us. A
member of the board of directors of an affiliate of Credit Suisse First Boston
is the Chairman and Chief Executive Officer of the general partner of Warburg
and an affiliate of Credit Suisse First Boston owns indirect minority economic
interests in the general partner of Warburg and the manager of Warburg.

     We have retained Innisfree M&A Incorporated to act as information agent and
EquiServe Trust Company, N.A. to act as depositary in connection with our offer.
The information agent may contact holders of shares by mail, telephone,
telegraph and in person and may request brokers, dealers, commercial banks,
trust companies and other nominee stockholders to forward materials relating to
our offer to beneficial owners. The information agent and the depositary will
each receive reasonable and customary compensation for their respective
services, will be reimbursed by us for specified reasonable out-of-pocket
expenses and will be indemnified against certain liabilities in connection with
our offer, including certain liabilities under the federal securities laws.
Innisfree M&A Incorporated has also been retained by us as proxy solicitors and
in connection with other communications by us to stockholders in connection with
North Fork's hostile offer. Information regarding Innisfree's arrangements with
us, as well as our arrangements with other public relations firms, is included
in the section entitled "Information Concerning Participants -- Other Persons"
in Annex A to our proxy statement for the 2000 annual stockholders meeting.

     Putnam Fiduciary Trust Company and Northern Trust Company act as the
trustees of our 401(k) savings plans and they and their tabulating agents will
be reimbursed for certain out-of-pocket costs in connection with our offer.

     No fees or commissions will be payable by us to brokers, dealers,
commercial banks or trust companies (other than fees to the parties described
above) for soliciting tenders of shares under our offer. Stockholders holding
shares through brokers or banks are urged to consult the brokers or banks to
determine whether transaction costs are applicable if stockholders tender shares
through such brokers or banks and not directly to the depositary. We, however,
upon request, will reimburse brokers, dealers, commercial banks and trust
companies for customary mailing and handling expenses incurred by them in
forwarding our offer and related materials to the beneficial owners of shares
held by them as a nominee or in a fiduciary capacity. No broker, dealer,
commercial bank or trust company has been authorized to act as our agent or as
an agent of either of the dealer managers, the information agent or the
depositary for purposes of our offer. We will pay or cause to be paid all stock
transfer taxes, if any, on our purchase of shares except as otherwise provided
in this document and Instruction 7 in the letter of transmittal.

SECTION 17.  MISCELLANEOUS.

     This offer to purchase and the related letter of transmittal will be mailed
to record holders of shares of our common stock and will be furnished to
brokers, dealers, commercial banks and trust companies whose names, or the names
of whose nominees, appear on our stockholder list or, if applicable, who are

                                       40
<PAGE>   44

listed as participants in a clearing agency's security position listing for
subsequent transmittal to beneficial owners of shares.

     We are not aware of any jurisdiction where the making of our offer is not
in compliance with applicable law. If we become aware of any jurisdiction where
the making of our offer or the acceptance of shares pursuant thereto is not in
compliance with applicable law, we will make a good faith effort to comply with
the applicable law. If, after such good faith effort, we cannot comply with the
applicable law, our offer will not be made to (nor will tenders be accepted from
or on behalf of) the holders of shares in such jurisdiction. In any jurisdiction
where the securities, blue sky or other laws require our offer to be made by a
licensed broker or dealer, our offer shall be deemed to be made on our behalf by
the dealer managers or one or more registered brokers or dealers licensed under
the laws of that jurisdiction.

     Pursuant to Rule 13e-4 promulgated under the Exchange Act, Dime has filed
with the SEC an Issuer Tender Offer Statement on Schedule TO which contains
additional information with respect to our offer. The Schedule TO, including the
exhibits and any amendments and supplements to that document, may be examined,
and copies may be obtained, at the same places and in the same manner as is set
forth in Section 10 with respect to information concerning us.

     WE HAVE NOT AUTHORIZED ANY PERSON TO MAKE ANY RECOMMENDATION ON OUR BEHALF
AS TO WHETHER YOU SHOULD TENDER OR NOT TENDER YOUR SHARES IN OUR OFFER. WE HAVE
NOT AUTHORIZED ANY PERSON TO GIVE ANY INFORMATION OR TO MAKE ANY REPRESENTATION
IN CONNECTION WITH OUR OFFER OTHER THAN THOSE CONTAINED IN THIS DOCUMENT OR IN
THE LETTER OF TRANSMITTAL. ANY RECOMMENDATION OR ANY SUCH INFORMATION OR
REPRESENTATION MADE BY ANYONE ELSE MUST NOT BE RELIED UPON AS HAVING BEEN
AUTHORIZED BY DIME, EITHER OF THE DEALER MANAGERS OR THE INFORMATION AGENT.

August 1, 2000

                                       41
<PAGE>   45

                        THE DEPOSITARY FOR OUR OFFER IS:

                         EQUISERVE TRUST COMPANY, N.A.

<TABLE>
<S>                                <C>                                     <C>
        By hand delivery:          By overnight delivery or express mail:        By first class mail:
 Securities Transfer & Reporting       EquiServe Trust Company, N.A.         EquiServe Trust Company, N.A.
         Services, Inc.                   Attn: Corporate Actions               Attn: Corporate Actions
c/o EquiServe Trust Company, N.A.           40 Campanelli Drive                       PO Box 9573
  100 William Street, Galleria              Braintree, MA 02184                  Boston, MA 02205-9573
       New York, NY 10038
</TABLE>

                      Facsimile Transmission: 781-575-4826

              Confirm Facsimile Receipt by telephone: 781-575-4816

     The letter of transmittal and certificates for shares and any other
required documents should be sent or delivered by each Dime stockholder or such
stockholder's broker, dealer, commercial bank, trust company or nominee to the
depositary at one of its addresses set forth above.

     Any questions or requests for assistance may be directed to the information
agent or either of the dealer managers at their respective telephone numbers and
addresses set forth below. Requests for additional copies of this offer to
purchase, the letter of transmittal or the notice of guaranteed delivery may be
directed to the information agent at the telephone number and address set forth
below. You may also contact your broker, dealer, commercial bank, trust company
or nominee for assistance concerning our offer. To confirm delivery of shares,
stockholders are directed to contact the depositary.

                    THE INFORMATION AGENT FOR OUR OFFER IS:

                           INNISFREE M&A INCORPORATED
                         501 Madison Avenue, 20th Floor
                            New York, New York 10022
                            Toll Free: 888-750-5835
              Banks and Brokerage Firms Please Call: 212-750-5833

                     THE DEALER MANAGERS FOR OUR OFFER ARE:

<TABLE>
<S>                         <C>
CREDIT SUISSE FIRST BOSTON        MERRILL LYNCH & CO.
       CORPORATION              4 World Financial Center
  Eleven Madison Avenue         New York, New York 10080
 New York, New York 10010      Call Collect: 212-236-3790
 Toll Free: 800-881-8320
</TABLE>


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