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

                               DIME BANCORP, INC.
                             LETTER OF TRANSMITTAL
                        TO TENDER SHARES OF COMMON STOCK
           (including the associated preferred stock purchase rights)
                                       of
                               DIME BANCORP, INC.
                       PURSUANT TO THE OFFER TO PURCHASE
                              DATED AUGUST 1, 2000

THIS 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.
DIME MAY EXTEND THE OFFER PERIOD AT ANY TIME.

                        The depositary for the offer is:

                         EQUISERVE TRUST COMPANY, N.A.

<TABLE>
<S>                                <C>                                <C>
             By Mail:                    By Overnight Delivery:               By Hand Delivery:
  EquiServe Trust Company, N.A.      EquiServe Trust Company, N.A.          Securities Transfer &
     Attn: Corporate Actions            Attn: Corporate Actions            Reporting Services, Inc.
           PO Box 9573                    40 Campanelli Drive         c/o EquiServe Trust Company, N.A.
      Boston, MA 02205-9573               Braintree, MA 02184            100 William Street, Galleria
                                                                              New York, NY 10038
</TABLE>

THIS LETTER OF TRANSMITTAL, INCLUDING THE ACCOMPANYING INSTRUCTIONS, SHOULD BE
READ CAREFULLY BEFORE THIS LETTER OF TRANSMITTAL IS COMPLETED.

FOR THIS LETTER OF TRANSMITTAL TO BE VALIDLY DELIVERED, IT MUST BE RECEIVED BY
THE DEPOSITARY AT ONE OF THE ABOVE ADDRESSES BEFORE THE OFFER EXPIRES (IN
ADDITION TO THE OTHER REQUIREMENTS DETAILED IN THIS LETTER AND ITS
INSTRUCTIONS). DELIVERY OF THIS LETTER OF TRANSMITTAL TO ANOTHER ADDRESS WILL
NOT CONSTITUTE A VALID DELIVERY. DELIVERIES TO DIME, EITHER OF THE DEALER
MANAGERS, THE INFORMATION AGENT OR THE BOOK-ENTRY TRANSFER FACILITY WILL NOT BE
FORWARDED TO THE DEPOSITARY AND WILL NOT CONSTITUTE A VALID DELIVERY.
<PAGE>   2

<TABLE>
<S>                                                          <C>           <C>           <C>
------------------------------------------------------------------------------------------------------
                                    DESCRIPTION OF SHARES TENDERED
------------------------------------------------------------------------------------------------------
      NAME(S) AND ADDRESS(ES) OF REGISTERED HOLDER(S)
        (IF BLANK, PLEASE FILL IN EXACTLY AS NAME(S)
                APPEAR(S) ON CERTIFICATE(S))                              SHARES TENDERED
------------------------------------------------------------------------------------------------------
                                                                  FOR CERTIFICATES
                                                                     TENDERED(1)
                                                              (Attach additional signed
                                                                 list if necessary.)
                                                             ---------------------------------------
                                                                           TOTAL NUMBER
                                                                             OF SHARES      NUMBER
                                                              CERTIFICATE  EVIDENCED BY    OF SHARES
                                                               NUMBER(S)   CERTIFICATE(S)  TENDERED(2)
                                                             ---------------------------------------

                                                             ---------------------------------------

                                                             ---------------------------------------

 Indicate in this box the order (by certificate number) in   ---------------------------------------
 which shares are to be purchased in event of proration      ---------------------------------------
 (attach additional signed list if necessary): (1)(3)        TOTAL CERTIFICATED
 1st:                                                        SHARES TENDERED
 2nd:                                                        ---------------------------------------
 3rd:                                                        TOTAL DIVIDEND REINVESTMENT
 4th:                                                        PROGRAM SHARES
                                                             TENDERED(4)
                                                             ---------------------------------------
                                                             TOTAL SHARES TENDERED
                                                             BY BOOK-ENTRY
                                                             ---------------------------------------
                                                             TOTAL SHARES TENDERED
------------------------------------------------------------------------------------------------------

 (1) Need not be completed if shares are delivered by book-entry transfer.
 (2) If you desire to tender fewer than all shares evidenced by any certificates listed, please
     indicate in this column the number of shares you wish to tender. Otherwise, all shares evidenced
     by such certificates will be deemed to have been tendered. See Instruction 4.
 (3) If you do not designate an order, in the event less than all shares tendered are purchased due to
     proration, shares will be selected for purchase by the depositary. See Instruction 9.
 (4) See box below regarding tendering dividend reinvestment program shares. See also Instruction 17.
------------------------------------------------------------------------------------------------------
</TABLE>

                                        2
<PAGE>   3

WHEN THIS LETTER OF TRANSMITTAL SHOULD BE USED:

     You should complete this letter of transmittal only if:

     - you are including with this letter certificates representing the shares
       that you are tendering (or the certificates will be delivered pursuant to
       a notice of guaranteed delivery you have previously sent to the
       depositary),

     - you are tendering shares held through the Dime Dividend Reinvestment and
       Optional Cash Purchase Program, or

     - you are concurrently tendering shares by book-entry transfer to the
       account maintained by the depositary at The Depository Trust Company (the
       "book-entry transfer facility") pursuant to section 3 of the offer to
       purchase and you are not (1) using an agent's message (as defined in
       Instruction 2) or (2) providing the acknowledgement required by the
       automated tender offer program.

     If you want to tender your shares into the offer but (1) your certificates
are not immediately available, (2) you cannot deliver all documents required by
this letter of transmittal to the depositary before the offer expires, or (3)
you cannot comply with the procedure for book-entry transfer on a timely basis,
you can still tender your shares if you comply with the guaranteed delivery
procedure set forth in section 3 of the offer to purchase. See Instruction 2.

     This letter of transmittal may not be used for shares held in the North
American Mortgage Company Retirement and 401(k) Savings Plan or the Retirement
401(k) Investment Plan of Dime Bancorp, Inc. If you are a participant in one of
these plans and want to tender some or all of the shares allocated to your plan
account, you must follow the instructions in the "Letter to Participants in the
North American Mortgage Company Retirement and 401(k) Savings Plan" or "Letter
to Participants in the Retirement 401(k) Investment Plan of Dime Bancorp, Inc."
and related materials sent separately. However, if you also own shares apart
from the plan and you want to tender some or all of them, you must also submit
this letter of transmittal to tender the non-plan shares. See Instruction 16.

                ADDITIONAL INFORMATION REGARDING TENDERED SHARES

[ ]  Check here if any certificate evidencing the shares you are tendering with
     this letter of transmittal has been lost, stolen, destroyed or mutilated.
     If so, you must complete an Affidavit of Loss and return it with your
     letter of transmittal. A bond may be required to be posted by you to secure
     against the risk that the certificates may be recirculated. Please call
     EquiServe Trust Company, N.A., as the transfer agent for the shares, at
     1-800-730-4001 to get an Affidavit of Loss, for further instructions and
     for a determination as to whether you will need to post a bond. See
     Instruction 14.

[ ]  Check here if tendered shares are being delivered by book-entry transfer
     made to an account maintained by the depositary with the book-entry
     transfer facility and complete the following (only financial institutions
     that are participants in the system of any book-entry transfer facility may
     deliver shares by book-entry transfer):

     Name of Tendering Institution:  ----------------------------------------

     Account Number:  -------------------------------------------------------

     Transaction Code Number:  ----------------------------------------------

[ ]  Check here if tendered shares are being delivered pursuant to a notice of
     guaranteed delivery previously sent to the depositary and complete the
     following:

     Name(s) of Registered Owner(s):  ---------------------------------------

     Date of Execution of Notice of Guaranteed Delivery  --------------------

     Name of Institution which Guaranteed Delivery:  ------------------------

     Account Number:  -------------------------------------------------------

                                        3
<PAGE>   4

 TENDER OF SHARES HELD IN DIME DIVIDEND REINVESTMENT AND OPTIONAL CASH PURCHASE
                                    PROGRAM
                              (SEE INSTRUCTION 17)

Complete this section if you want to tender shares held in Dime's dividend
reinvestment program. Please check only one box. If you check more than one box,
or you check the second box but do not indicate a number of shares, none of the
shares held in your dividend reinvestment program account will be tendered.

[ ]  I instruct the program administrator to tender ALL of the shares credited
     to my dividend reinvestment program account.

[ ]  I instruct the program administrator to tender the following number of
     shares credited to my dividend reinvestment program account.

               Number of shares: ________________

                        PRICE AT WHICH YOU ARE TENDERING
                              (SEE INSTRUCTION 5)

You must check one box and only one box if you want to tender your shares. If
more than one box is checked or if no box is checked, your shares will not be
properly tendered.

SHARES TENDERED AT A PRICE DETERMINED BY YOU:

By checking one of the following boxes below instead of the box under "Shares
tendered at a price determined pursuant to the offer," you are tendering shares
at the price checked. This action could result in none of your shares being
purchased if the purchase price selected by Dime for the shares is less than the
price checked below. If you want to tender portions of your shares at more than
one price, you must complete a separate letter of transmittal for each price at
which you tender shares. The same shares cannot be tendered at more than one
price.

        PRICE (IN DOLLARS) PER SHARE AT WHICH SHARES ARE BEING TENDERED

<TABLE>
<S>  <C>      <C>  <C>      <C>  <C>      <C>  <C>
[ ]  $16.000  [ ]  $16.500  [ ]  $17.000  [ ]  $17.500
[ ]  $16.125  [ ]  $16.625  [ ]  $17.125  [ ]  $17.625
[ ]  $16.250  [ ]  $16.750  [ ]  $17.250  [ ]  $17.750
[ ]  $16.375  [ ]  $16.875  [ ]  $17.375  [ ]  $17.875
                     [ ] $18.000
</TABLE>

                                       OR

SHARES TENDERED AT A PRICE DETERMINED PURSUANT TO THE OFFER:

[ ]  By checking this one box instead of one of the price boxes above, you are
     tendering shares and are willing to accept the purchase price selected by
     Dime in accordance with the terms of the offer. This action will maximize
     the chance of having Dime purchase your shares (subject to the possibility
     of proration). Note this action could result in your receiving a price per
     share as low as $16.00.

                                        4
<PAGE>   5

                                    ODD LOTS
                              (SEE INSTRUCTION 8)

Complete this section only if you own, or are tendering on behalf of a person
who owns, beneficially or of record, an aggregate of fewer than 100 shares
(including any shares held in Dime's dividend reinvestment program, but not
including any shares held in the North American Mortgage Company Retirement and
401(k) Savings Plan or the Retirement 401(k) Investment Plan of Dime Bancorp,
Inc.) and are tendering all of your shares.

You either (check one box):

[ ]  are the beneficial or record owner of an aggregate of fewer than 100
     shares, all of which are being tendered; or

[ ]  are a broker, dealer, commercial bank, trust company, or other nominee that
     (a) is tendering for the beneficial owner(s), shares with respect to which
     it is the record holder, and (b) believes, based upon representations made
     to it by the beneficial owner(s), that each such person is the beneficial
     owner of an aggregate of fewer than 100 shares and is tendering all of the
     shares.

                                        5
<PAGE>   6

                               CONDITIONAL TENDER
                              (SEE INSTRUCTION 15)

You may condition your tender of shares on Dime purchasing a specified minimum
number of your tendered shares, all as described in section 6 of the offer to
purchase. Unless the minimum number of shares you indicate below is purchased by
Dime in the offer, none of the shares you tendered will be purchased. It is your
responsibility to calculate that minimum number of shares that must be purchased
if any are purchased, and you are urged to consult your own tax advisor before
completing this section. Unless this box has been checked and a minimum number
of shares specified, your tender will be deemed unconditional.

[ ]  The minimum number of shares that must be purchased, if any are purchased,
     is: ______ shares.

If because of proration, the minimum number of shares that you designated above
will not be purchased, Dime may accept conditional tenders by random lot, if
necessary. However, to be eligible for purchase by random lot, you must have
tendered all your shares and checked this box:

[ ]  The tendered shares represent all shares held by me.

<TABLE>
<S> <C>                                                   <C>
-------------------------------------------------------------
    SPECIAL PAYMENT INSTRUCTIONS
    (SEE INSTRUCTIONS 1, 6, 7 AND 10)

    Complete this box only if you want certificate(s) for
    shares not tendered or not purchased and/or any check
    for the purchase price to be issued in the name of
    someone other than you, or if you want shares that
    you delivered by book-entry transfer to be returned
    by credit to an account at the book-entry transfer
    facility other than the one designated earlier.
    Issue: [ ] Check
           [ ] Certificate(s)
    to:

    Name: -----------------------------------------------
                       (Please Print)

    Address:
    ---------------------------------------------

    -----------------------------------------------------
                     (Include Zip Code)

    -----------------------------------------------------
       (Tax Identification or Social Security Number)
                  (See Substitute Form W-9)
    [ ]  Credit shares delivered by book-entry transfer
    and not purchased to the account set forth below:

    Account Number: ------------------------------------
-------------------------------------------------------------
</TABLE>

<TABLE>
<S> <C>                                                   <C>
-------------------------------------------------------------
    SPECIAL DELIVERY INSTRUCTIONS
    (SEE INSTRUCTIONS 1, 6, 7 AND 10)

    Complete this box only if you want certificate(s) for
    shares not tendered or not purchased and/or any check
    for the purchase price to be mailed or sent to
    someone other than you or to you at an address other
    than that designated earlier.
    Mail:  [ ] Check
            [ ] Certificate(s)
                             to:

    Name: -----------------------------------------------
                       (Please Print)

                          Address:
        ---------------------------------------------
    -----------------------------------------------------
                     (Include Zip Code)

-------------------------------------------------------------
</TABLE>

Dime has no obligation, pursuant to the "Special Payment Instructions," to
transfer any certificate for shares from the name of its registered holder(s),
or to order the registration or transfer of any shares tendered by book-entry
transfer, if Dime does not purchase any of the shares represented by such
certificate or tendered by such book-entry transfer.

                                        6
<PAGE>   7

           NOTE: SIGNATURES MUST BE PROVIDED IN THE BOX BELOW LABELED
    "IMPORTANT -- STOCKHOLDERS SIGN HERE" IF YOU WANT TO TENDER YOUR SHARES.
              PLEASE READ THE ACCOMPANYING INSTRUCTIONS CAREFULLY.

To EquiServe Trust Company, N.A.:

     The undersigned hereby tenders to Dime Bancorp, Inc., a Delaware
corporation, the above-described shares of Dime's common stock, $0.01 par value
per share, at the price per share indicated in this letter of transmittal, net
to the seller in cash, without interest, upon the terms and subject to the
conditions set forth in the offer to purchase, dated August 1, 2000, receipt of
which is hereby acknowledged, and in this letter of transmittal which, as
amended or supplemented from time to time, together constitute the offer. All
shares tendered and purchased will include the associated preferred stock
purchase rights issued pursuant to the Stockholder Protection Rights Agreement,
dated as of October 20, 1995, as amended, between Dime and The Dime Savings Bank
of New York, FSB, as rights agent, and, unless the context otherwise requires,
all references to shares include the associated preferred stock purchase rights.

     Subject to, and effective upon, acceptance for payment of the shares
tendered in accordance with the terms and subject to the conditions of the
offer, including, if the offer is extended or amended, the terms and conditions
of the extension or amendment, the undersigned agrees to sell, assign and
transfer to, or upon the order of, Dime all right, title and interest in and to
all shares tendered and orders the registration of all shares if tendered by
book-entry transfer and irrevocably constitutes and appoints the depositary as
the true and lawful agent and attorney-in-fact of the undersigned with respect
to the shares with full knowledge that the depositary also acts as the agent of
Dime, with full power of substitution (the power of attorney being deemed to be
an irrevocable power coupled with an interest), to:

          1.  deliver certificate(s) representing the shares or transfer
     ownership of the shares on the account books maintained by the book-entry
     transfer facility, together, in either case, with all accompanying
     evidences of transfer and authenticity, to or upon the order of Dime upon
     receipt by the depositary, as the undersigned's agent, of the purchase
     price with respect to the shares;

          2.  present certificates for the shares for cancellation and transfer
     on Dime's books; and

          3.  receive all benefits and otherwise exercise all rights of
     beneficial ownership of the shares, subject to the next paragraph, all in
     accordance with the terms and subject to the conditions of the offer.

     The undersigned covenants, represents and warrants to Dime that:

          1.  the undersigned has full power and authority to tender, sell,
     assign and transfer the shares tendered hereby and when and to the extent
     accepted for payment, Dime will acquire good, marketable and unencumbered
     title to the tendered shares, free and clear of all security interests,
     liens, restrictions, charges, encumbrances, conditional sales agreements or
     other obligations relating to the sale or transfer of the shares, and not
     subject to any adverse claims;

          2.  the undersigned understands that tenders of shares pursuant to any
     one of the procedures described in section 3 of the offer to purchase and
     in the instructions to this letter of transmittal will constitute the
     undersigned's acceptance of the terms and conditions of the offer,
     including the undersigned's representation and warranty that (a) the
     undersigned has a "net long position," within the meaning of Rule 14e-4
     promulgated under the Securities Exchange Act of 1934, in the shares or
     equivalent securities at least equal to the shares being tendered, and (b)
     the tender of shares complies with Rule 14e-4;

          3.  the undersigned will, upon request, execute and deliver any
     additional documents deemed by the depositary or Dime to be necessary or
     desirable to complete the sale, assignment and transfer of the shares
     tendered; and

          4.  the undersigned has read, understands and agrees to all of the
     terms of the offer.

                                        7
<PAGE>   8

     The undersigned understands that Dime's acceptance of shares tendered
pursuant to any one of the procedures described in section 3 of the offer to
purchase and in the instructions to this letter of transmittal will constitute a
binding agreement between the undersigned and Dime upon the terms and subject to
the conditions of the offer. The undersigned acknowledges that under no
circumstances will Dime pay interest on the purchase price, including without
limitation, by reason of any delay in making payment.

     The name(s) and address(es) of the registered holder(s) should be printed,
if they are not already printed above, exactly as they appear on the
certificates evidencing shares tendered. The certificate numbers, the number of
shares evidenced by the certificates, the number of shares that the undersigned
wishes to tender, and the price at which the shares are being tendered should be
set forth in the appropriate boxes above.

     The undersigned understands that Dime will determine a single per share
price, not greater than $18.00 nor less than $16.00, that it will pay for shares
properly tendered, taking into account the number of shares tendered and the
prices specified by tendering stockholders. Dime will select the lowest purchase
price that will allow it to buy 13,607,664 shares or, if a lesser number of
shares are properly tendered, all shares that are properly tendered and not
properly withdrawn. All shares acquired in the offer will be acquired at the
same purchase price. All shares properly tendered at prices equal to or below
the purchase price and not properly withdrawn will be purchased, subject to the
conditions of the offer and the "odd lot" priority, proration and conditional
tender provisions described in the offer to purchase. Shares tendered at prices
in excess of the purchase price that is selected by Dime and shares not
purchased because of proration or conditional tenders will be returned without
expense to the stockholder.

     The undersigned recognizes that under the circumstances set forth in the
offer to purchase Dime may terminate or amend the offer or may postpone the
acceptance for payment of, or the payment for, shares tendered or may accept for
payment fewer than all of the shares tendered. The undersigned understands that
certificate(s) for any shares not tendered or not purchased will be returned to
the undersigned at the address indicated above, unless otherwise indicated in
the box entitled "Special Payment Instructions" or the box entitled "Special
Delivery Instructions" above. The undersigned acknowledges that Dime has no
obligation, pursuant to the "Special Payment Instructions" box, to transfer any
certificate for shares from the name of its registered holder(s), or to order
the registration or transfer of any shares tendered by book-entry transfer, if
Dime does not purchase any of the shares represented by such certificate or
tendered by such book-entry transfer.

     The check for the aggregate net purchase price for the shares tendered and
purchased will be issued to the order of the undersigned and mailed to the
address indicated above, unless otherwise indicated in the boxes entitled
"Special Payment Instructions" or "Special Delivery Instructions" above.

     All authority conferred or agreed to be conferred by this letter of
transmittal will survive the death or incapacity of the undersigned, and any
obligation of the undersigned will be binding on the heirs, personal
representatives, executors, administrators, successors, assigns, trustees in
bankruptcy and legal representatives of the undersigned. Except as stated in the
offer to purchase, this tender is irrevocable.

                                        8
<PAGE>   9

                                   IMPORTANT

                             STOCKHOLDERS SIGN HERE
         (PLEASE COMPLETE AND RETURN THE ATTACHED SUBSTITUTE FORM W-9.)

(Must be signed by the registered holder(s) exactly as such holder(s) name(s)
appear(s) on certificate(s) for shares or on a security position listing or by
person(s) authorized to become the registered holder(s) thereof by certificates
and documents transmitted with this letter of transmittal. If signature is by a
trustee, executor, administrator, guardian, attorney-in-fact, officer of a
corporation or other person acting in a fiduciary or representative capacity,
please set forth full title and see Instruction 6.)

--------------------------------------------------------------------------------

--------------------------------------------------------------------------------
                           (Signature(s) of Owner(s))

Dated:                                , 2000
      ------------------------------------

Name(s):------------------------------------------------------------------------

        ------------------------------------------------------------------------
                                     (Please Print)

Capacity (full title):
                 ---------------------------------------------------------------

Address:
       -------------------------------------------------------------------------

       -------------------------------------------------------------------------
                                  (Include Zip Code)

Daytime Area Code and Telephone Number:
                                    --------------------------------------------

Tax Identification or Social Security Number:
                                     -------------------------------------------

                           (SEE SUBSTITUTE FORM W-9)

              GUARANTEE OF SIGNATURE(S) (SEE INSTRUCTIONS 1 AND 6)

Authorized Signature:
                 ---------------------------------------------------------------

Name:
      --------------------------------------------------------------------------
                                    (Please Print)

Title:
     ---------------------------------------------------------------------------

Name of Firm:
            --------------------------------------------------------------------

Address:
       -------------------------------------------------------------------------
                                  (Include Zip Code)

Area Code and Telephone Number:
                             ---------------------------------------------------
Dated:                               , 2000
      ------------------------------------

                                        9
<PAGE>   10

<TABLE>
<CAPTION>
<S>                       <C>                                                    <C>
PAYER: EQUISERVE TRUST COMPANY, N.A.
----------------------------------------------------------------------------------------------------------------------
SUBSTITUTE                 PART I -- TAXPAYER IDENTIFICATION NUMBER -- FOR ALL   ----------------------------
 FORM W-9                  ACCOUNTS, ENTER TAXPAYER IDENTIFICATION NUMBER IN     Social security number
 DEPARTMENT OF             THE BOX AT RIGHT AND CERTIFY BY SIGNING AND DATING    OR
 THE TREASURY              BELOW.                                                ----------------------------
 INTERNAL REVENUE          Note: If the account is in more than one name, see    Employer identification number
 SERVICE                   the chart in the enclosed guidelines to determine
                           which number to give the payer.
                          ------------------------------------------------------------------------------------------
</TABLE>

<TABLE>
<S>                      <C>
                          PART II -- For payees exempt from backup withholding, please write "EXEMPT" here (see
                          the enclosed guidelines):
                          -------------------------------------------------------------------------------------
                         ---------------------------------------------------------------------------------------

PAYER'S REQUEST           PART III -- Certification -- UNDER PENALTIES OF PERJURY, I CERTIFY THAT (1) The number
 FOR TAXPAYER             shown on this form is my correct Taxpayer Identification Number (or I am waiting for a
 NUMBER (TIN)             number to be issued to me), and (2) I am not subject to backup withholding because:
                          (a) I am exempt from backup withholding, or (b) I have not been notified by the
                          Internal Revenue Service (the "IRS") that I am subject to backup withholding as a
                          result of a failure to report all interest or dividends or (c) the IRS has notified me
                          that I am no longer subject to backup withholding.
                         ---------------------------------------------------------------------------------------

                          Certification Instructions -- You must cross out item (2) above if you have been
                          notified by the IRS that you are currently subject to backup withholding because of
                          underreporting of interest or dividends on your tax return and you have not been
                          notified by the IRS that you are no longer subject to backup withholding. (Also, see
                          instructions in the enclosed guidelines.)
                          Signature: --------------------------------------------------------
                          Date:--------------------------, 2000
----------------------------------------------------------------------------------------------------------------
</TABLE>

NOTE:  Failure to complete and return this form may result in backup withholding
of 31% of any payments made to you pursuant to the offer. Please review the
enclosed guidelines for certification of taxpayer identification number on
Substitute Form W-9 for additional details. You must complete the following
certificate if you are awaiting (or will soon apply for) a taxpayer
identification number.

             CERTIFICATE OF AWAITING TAXPAYER IDENTIFICATION NUMBER

     I certify under penalties of perjury that a taxpayer identification number
has not been issued to me, and that I mailed or delivered an application to
receive a taxpayer identification number to the appropriate Internal Revenue
Service Center or Social Security Administration Office (or I intend to mail or
deliver an application in the near future). I understand that, notwithstanding
the information I provided in Part III of the Substitute Form W-9 above (and the
fact that I have completed this Certificate of Awaiting Taxpayer Identification
Number), if I do not provide a taxpayer identification number to the depositary
within sixty (60) days, the depositary is required to withhold 31% of all cash
payments made to me thereafter until I provide a number.

Signature ------------------------------                  Date: ----------, 2000

Name (Please Print)
--------------------------------------------------------------------------------

Address (Please Print)
--------------------------------------------------------------------------------

                                       10
<PAGE>   11

                                  INSTRUCTIONS
             FORMING PART OF THE TERMS AND CONDITIONS OF THE OFFER.

     1.  GUARANTEE OF SIGNATURES.  Depending on how the certificates for your
shares are registered and to whom you want payments or deliveries made, you may
need to have the signatures on this letter of transmittal guaranteed by an
eligible guarantor institution. No signature guarantee is required if either:

     - this letter of transmittal is signed by the registered holder(s) of the
       shares tendered (which, for these purposes, includes any participant in
       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(s) 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 of the boxes entitled "Special Payment
       Instructions" or "Special Delivery Instructions" above; or

     - the shares are tendered for the account of a bank, broker, dealer, credit
       union, savings association or other entity which 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 which
       is an "eligible guarantor institution," as that term is defined in Rule
       17Ad-15 promulgated under the Securities Exchange Act of 1934, as
       amended.

     In all other cases, including if you have completed either the box entitled
"Special Payment Instructions" or "Special Delivery Instructions" above, an
eligible guarantor institution must guarantee all signatures on this letter of
transmittal. You may also need to have any certificates you deliver endorsed or
accompanied by a stock power, and the signatures on these documents also may
need to be guaranteed. See Instruction 6.

     2.  DELIVERY OF LETTER OF TRANSMITTAL AND CERTIFICATES; GUARANTEED DELIVERY
PROCEDURES.  For your shares to be properly tendered, either (1) or (2) below
must happen:

     (1) The depositary must receive all of the following at its address above
         in this letter of transmittal before or on the date Dime's offer
         expires:

        - one of (a) the certificates for the shares, (b) a confirmation of
          receipt of the shares pursuant to the procedure for book-entry
          transfer described in this Instruction 2 or (c) in the case of shares
          held in the Dime dividend reinvestment program, completion of the
          appropriate sections of this letter of transmittal; and

        - one of (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 described in this
          Instruction 2 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" described in this Instruction 2, and

        - any other documents required by this letter of transmittal.

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

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

     Agent's Message.  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 this letter of transmittal and that Dime may enforce such
agreement against them.

     Automated Tender Offer Program.  Participants in the book-entry transfer
facility may also tender their shares in accordance with the automated tender
offer program to the extent it is available to them for the shares

                                       11
<PAGE>   12

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 this letter of transmittal and that we may enforce such agreement
against them.

     Guaranteed Delivery.  If you want to tender your shares but your share
certificate(s) are not immediately available or cannot be delivered to the
depositary before the offer expires, 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 offer expires, your shares may
still be tendered, 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 provided with this
       letter of transmittal, 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
        described in this Instruction 2 or (c) in the case of shares held in the
        Dime dividend reinvestment program, completion of the appropriate
        sections of this 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 described in this
        Instruction 2 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" described in this Instruction 2, and

      - any other documents required by this 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. IN ALL CASES, SUFFICIENT TIME SHOULD BE
ALLOWED TO ENSURE TIMELY DELIVERY.

     Except as specifically permitted by section 6 of the offer to purchase,
Dime will not accept any alternative, conditional or contingent tenders, nor
will it purchase any fractional shares, except as expressly provided in the
offer to purchase. All tendering stockholders, by execution of this letter of
transmittal or a manually signed facsimile of this letter of transmittal, waive
any right to receive any notice of the acceptance of their tender.

     3.  INADEQUATE SPACE.  If the space provided in the box entitled
"Description of Shares Tendered" above is inadequate, the certificate numbers
and/or the number of shares should be listed on a separate signed schedule and
attached to this letter of transmittal.

     4.  PARTIAL TENDERS AND UNPURCHASED SHARES.  (This paragraph does not apply
to stockholders who tender by book-entry transfer.) If fewer than all of the
shares evidenced by any certificate are to be tendered, fill in the number of
shares that are to be tendered in the column entitled "Number of Shares
Tendered" in the box entitled "Description of Shares Tendered" above. In that
case, if any tendered shares are purchased, a new certificate for the remainder
of the shares (including any shares not purchased) evidenced by the old
certificate(s) will be issued and sent to the registered holder(s), unless
otherwise specified in either the box entitled "Special Payment Instructions" or
"Special Delivery Instructions" in this letter of transmittal, as soon as
practicable after the expiration date. Unless otherwise indicated, all shares
represented by the certificate(s) set forth above and delivered to the
depositary will be deemed to have been tendered.

     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 the tender offer or the proper withdrawal
of the shares, as applicable. In
                                       12
<PAGE>   13

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.

     5.  INDICATION OF PRICE AT WHICH SHARES ARE BEING TENDERED.  If you want to
tender your shares you must properly complete the pricing section of this letter
of transmittal, which is called "Price At Which You Are Tendering". You must
check one box in the pricing section. If more than one box is checked or no box
is checked, your shares will not be properly tendered. If you want to tender
portions of your shares at more than one price, you must complete a separate
letter of transmittal for each price at which you tender shares. However, the
same shares cannot be tendered at more than one price, unless previously and
properly withdrawn as provided in section 4 of the offer to purchase.

     6.  SIGNATURES ON LETTER OF TRANSMITTAL; STOCK POWERS AND ENDORSEMENTS.

     Exact Signature.  If this letter of transmittal is signed by the registered
holder(s) of the shares tendered, the signature(s) must correspond exactly with
the name(s) as written on the face of the certificate(s) without any change
whatsoever.

     Joint Holders.  If the shares tendered are registered in the names of two
or more joint holders, each holder must sign this letter of transmittal.

     Different Names on Certificates.  If any tendered shares are registered in
different names on several certificates, it will be necessary to complete, sign
and submit as many separate letters of transmittal (or manually signed
facsimiles) as there are different registrations of certificates.

     Endorsements.  When this letter of transmittal is signed by the registered
holder(s) of the shares tendered, no endorsements of certificates representing
the shares or separate stock powers are required unless payment is to be made or
the certificates for shares not tendered or not purchased are to be issued to a
person other than the registered holder(s). Signature(s) on the certificate(s)
must be guaranteed by an eligible institution.

     If this letter of transmittal is signed by a person other than the
registered holder(s) of the certificates listed, or if payment is to be made or
certificates for shares not tendered or not purchased are to be issued to a
person other than the registered holder(s), the certificates must be endorsed or
accompanied by appropriate stock powers, in either case signed exactly as the
name(s) of the registered holder(s) appears on the certificates, and the
signatures on the certificates or stock powers must be guaranteed by an eligible
institution. See Instruction 1.

     Signatures of Fiduciaries.  If this letter of transmittal or any
certificate or stock power is signed by a trustee, executor, administrator,
guardian, attorney-in-fact, officer of a corporation or any other person acting
in a fiduciary or representative capacity, that person should so indicate when
signing and must submit proper evidence satisfactory to Dime of his or her
authority to so act.

     7.  STOCK TRANSFER TAXES.  Except as provided in this Instruction 7, no
stock transfer tax stamps or funds to cover tax stamps need accompany this
letter of transmittal. Dime will pay any stock transfer taxes payable on the
transfer to it of shares purchased pursuant to the offer. If, however, (a)
payment of the purchase price is to be made to any person other than the
registered holder(s); (b) shares not tendered or rejected for purchase are to be
registered in the name(s) of any person(s) other than the registered holder(s);
or (c) certificates representing tendered shares are registered in the name(s)
of any person(s) other than the person(s) signing this letter of transmittal,
then the depositary will deduct from the purchase price the amount of any stock
transfer taxes (whether imposed on the registered holder(s), other person(s) or
otherwise) payable on account of the transfer to that person, unless
satisfactory evidence of the payment of the taxes or any exemption therefrom is
submitted.

     8. ODD LOTS.  If Dime is to purchase fewer than all shares properly
tendered and not properly withdrawn, the shares purchased first will consist of
all shares properly tendered by any stockholder who owns, beneficially or of
record, an aggregate of fewer than 100 shares (including shares held in Dime's
dividend reinvestment program, but not including any shares held in the North
American Mortgage Company Retirement and 401(k) Savings Plan or the Retirement
401(k) Investment Plan of Dime Bancorp, Inc.) and who tenders all of the
                                       13
<PAGE>   14

holder's shares at or below the purchase price. This preference will not be
available unless the section captioned "Odd Lots" is completed.

     9. ORDER OF PURCHASE IN EVENT OF PRORATION.  As described in section 1 of
the offer to purchase, stockholders can specify in the "Description of Shares
Tendered" box of this letter of transmittal the order in which specified
portions of their shares will be purchased if, as a result of the proration
provisions or otherwise, some but not all of the tendered shares are purchased
in the tender offer. The order of purchase may have an effect on the federal
income tax treatment of the purchase price for the shares purchased. See
sections 1 and 14 of the offer to purchase.

     10. SPECIAL PAYMENT AND DELIVERY INSTRUCTIONS.  If certificate(s) for
shares not tendered or not purchased and/or check(s) are to be issued in the
name of a person other than the signer of this letter of transmittal or if the
certificates and/or checks are to be sent to someone other than the person
signing this letter of transmittal or to the signer at a different address, the
box entitled "Special Payment Instructions" and/or the box entitled "Special
Delivery Instructions" on this letter of transmittal should be completed as
applicable and signatures must be guaranteed as described in Instruction 1.

     11. IRREGULARITIES.  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 Dime in its sole discretion and that
determination will be final and binding on all parties. Dime reserves the
absolute right to reject any or all tenders of any shares that it determines are
not in proper form or the acceptance for payment of or payment for which it
determines may be unlawful. Dime also reserves the absolute right to waive any
of the conditions of the tender offer or any defect or irregularity in any
tender with respect to any particular shares or any particular stockholder, and
Dime's interpretation of the terms of the tender offer (including these
Instructions) 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 Dime. Unless waived, any
defects and irregularities in connection with tenders must be cured within the
time period, if any, Dime determines. Neither Dime, 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
tender or incur any liability for failure to give any such notification.

     12. QUESTIONS AND REQUESTS FOR ASSISTANCE AND ADDITIONAL COPIES.  Questions
and requests for additional copies of the 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 the back page of
the offer to purchase and set forth below.

     13. TAX IDENTIFICATION NUMBER AND BACKUP WITHHOLDING.  Federal income tax
law generally requires that a stockholder whose tendered shares are accepted for
purchase, or the stockholder's assignee (in either case, the "payee"), provide
the depositary with the payee's correct Taxpayer Identification Number ("TIN"),
which, in the case of a payee who is an individual, is the payee's social
security number. If the depositary is not provided with the correct TIN or an
adequate basis for an exemption, the payee may be subject to penalties imposed
by the IRS and backup withholding in an amount equal to 31% of the gross
proceeds received pursuant to the offer. If withholding results in an
overpayment of taxes, a refund may be obtained.

     To prevent backup withholding, each payee must provide the payee's correct
TIN by completing the Substitute Form W-9 set forth in this letter of
transmittal, certifying that the TIN provided is correct (or that the payee is
awaiting a TIN) and that

     - the payee is exempt from backup withholding,

     - the payee has not been notified by the Internal Revenue Service that the
       payee is subject to backup withholding as a result of a failure to report
       all interest or dividends, or

     - the Internal Revenue Service has notified the payee that the payee is no
       longer subject to backup withholding.

     If the payee lacks a TIN, the payee should
                                       14
<PAGE>   15

     - consult the enclosed Guidelines for Certification of Taxpayer
       Identification Number on Substitute Form W-9 for instructions on applying
       for a TIN,

     - write "Applied For" in the space provided in Part 1 of the Substitute
       Form W-9, and

     - sign and date the Substitute Form W-9 and the Certificate of Awaiting
       Taxpayer Identification Number set forth in this document.

If the payee does not provide the payee's TIN to the depositary within sixty
(60) days, backup withholding will begin and continue until the payee furnishes
the payee's TIN to the depositary. Note that writing "Applied For" on the
Substitute Form W-9 means that the payee has already applied for a TIN or that
the payee intends to apply for one in the near future.

     If shares are held in more than one name or are not in the name of the
actual owner, consult the W-9 guidelines for information on which TIN to report.

     Exempt payees (including, among others, all corporations and certain
foreign individuals) are not subject to backup withholding and reporting
requirements. To prevent possible erroneous backup withholding, an exempt payee
should write "Exempt" in Part 2 of the Substitute Form W-9. See the enclosed W-9
guidelines for additional instructions. In order for a nonresident alien or
foreign entity to qualify as exempt, that person must submit a completed IRS
Form W-8 Certificate of Foreign Status or a Substitute Form W-8, signed under
penalty of perjury attesting to the exempt status. This form may be obtained
from the depositary.

     Non-United States holders are urged to consult their tax advisors regarding
the application of United States federal income tax withholding, including
eligibility for a withholding tax reduction or exemption, and the refund
procedure.

     14. LOST, STOLEN, DESTROYED OR MUTILATED 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 this 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.

     15. CONDITIONAL TENDERS.  As described in section 6 of the offer to
purchase, you may tender shares subject to the condition that all or a specified
minimum number of your shares tendered pursuant to this letter of transmittal or
a notice of guaranteed delivery must be purchased if any shares tendered are
purchased.

     If you wish to make a conditional tender you must indicate this in the box
captioned "Conditional Tender" in this letter of transmittal or, if applicable,
the notice of guaranteed delivery. In the box in this 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.

     As discussed in section 6 of the offer to purchase, proration may affect
whether Dime accepts conditional tenders and may result in shares tendered
pursuant to a conditional tender being deemed withdrawn if the minimum number of
shares would not be purchased. If, because of proration, the minimum number of
shares that you designate will not be purchased, Dime may accept conditional
tenders by random lot, if necessary. However, to be eligible for purchase by
random lot, you must have tendered all your shares and check the box so
indicating. Upon selection by lot, if any, Dime will limit its purchase in each
case to the designated minimum number of shares.

     All tendered shares will be deemed unconditionally tendered unless the
"Conditional Tender" box is completed.

     The conditional tender alternative is made available so that a stockholder
may seek to structure the purchase of shares pursuant to the 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
                                       15
<PAGE>   16

purposes. 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.
It is the tendering stockholder's responsibility to calculate the minimum number
of shares that must be purchased from the stockholder in order for the
stockholder to qualify for sale rather than dividend treatment. Each stockholder
is urged to consult his or her own tax advisor.

     16. 401(k) SAVINGS PLANS.  Participants in the North American Mortgage
Company Retirement and 401(k) Savings Plan or the Retirement 401(k) Investment
Plan of Dime Bancorp, Inc. may not use this letter of transmittal to direct the
tender of shares allocated to their 401(k) savings plan accounts, but must
comply with the instructions found in either the "Letter to Participants in the
North American Mortgage Company Retirement and 401(k) Savings Plan" or the
"Letter to Participants in the Retirement 401(k) Investment Plan of Dime
Bancorp, Inc." sent separately to them. Participants in these 401(k) savings
plans are urged to carefully read these letters and related materials sent to
them. Participants in these 401(k) savings plans who would like to tender shares
held outside of their 401(k) savings plan must use this letter of transmittal to
tender those shares held outside of the 401(k) savings plan.

     17. DIVIDEND REINVESTMENT PROGRAM.  If you want to tender shares of Dime
common stock held in your program account under Dime's dividend reinvestment
program, you must

     - complete the box in this letter of transmittal entitled "Tender of Shares
       Held in Dime Dividend Reinvestment and Optional Cash Purchase Program" by
       choosing the option to tender all of your shares in the program account
       or the option to tender a specific number of shares held in your program
       account (if the box is not completed, no shares held in your program
       account will be tendered), and

     - indicate the number of shares being tendered from the dividend
       reinvestment program account in the box in this letter of transmittal
       entitled "Description of Shares Tendered."

     As with shares held outside the dividend reinvestment program, you may
submit portions of the shares held in your dividend reinvestment program account
at different prices, but you must complete a separate letter of transmittal for
each price at which you tender shares. However, the same shares cannot be
tendered at more than one price, unless previously and properly withdrawn as
provided in section 4 of the offer to purchase.

     Shares held in a dividend reinvestment program account are counted as being
owned beneficially or of record when calculating whether a stockholder is an odd
lot holder. If a participant in the dividend reinvestment program is an odd lot
holder and wants to obtain the benefit of the odd lot priority, the participant
must complete the box in this letter of transmittal entitled "Odd Lots" and must
tender all of the holder's shares held both in the holder's dividend
reinvestment program account and outside such account.

     Please note that you need to be the record holder of at least 100 shares to
be able to participate in the dividend reinvestment portion of the program,
although you only need to be the record holder of at least one share to
participate in the optional cash purchase portion of the program. If your share
ownership falls below 100 shares by means of the tender and purchase of a
portion of your shares in the tender offer, you may not be able to participate
in the dividend reinvestment program.

     If you tender shares held in your dividend reinvestment plan program
account, all such shares credited to your program account, including fractional
shares, will be tendered, unless otherwise specified in the box entitled "Tender
of Shares Held in Dime Dividend Reinvestment and Optional Cash Purchase
Program."

                                       16
<PAGE>   17

                   The information agent for Dime's offer is:

                           INNISFREE M&A INCORPORATED
                         501 Madison Avenue, 20th Floor
                            New York, New York 10022
                           Toll Free: 1-888-750-5835
              Banks and Brokerage Firms please call: 212-750-5833

                   The dealer managers for Dime's 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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