<PAGE>

                                                                    EXHIBIT 10.1

            [LETTERHEAD OF THE DIME SAVINGS BANK OF NEW YORK, FSB]

                                 August 2, 1996



Mr. James M. Large, Jr.
14 Underhill Road
Locust Valley, New York 11560

Dear Jim:

     As you discussed with the Board of Directors of The Dime Savings Bank of
New York, FSB (the "Bank") at its meeting on June 28, 1996, you will be retiring
from your employment with the Bank and Dime Bancorp, Inc. (the "Company") on
December 31, 1996.  This Letter Agreement is intended to set forth certain items
regarding your employment by the Bank and the Company during the period from
June 28, 1996 through December 31, 1996, and to detail certain of the benefits
that will be provided to you upon your termination of employment by retirement
on December 31, 1996.

     Between now and December 31, 1996, the terms of your employment will
continue to be governed by the terms of the Amended and Restated Employment
Agreement between you and Anchor Savings Bank FSB ("Anchor"), dated as of
October 31, 1994, as assumed by The Dime Savings Bank of New York, FSB (the
"Prior Bank Agreement"), and the related Amended Agreement between you and
Anchor Bancorp, Inc., dated as of October 31, 1994, as assumed by the Company
(the "Prior Company Agreement"), provided, however, that the benefits to be
provided to you in connection with and following your retirement on December 31,
1996 shall be as provided herein rather than those that would otherwise be
provided pursuant to the terms of the Prior Bank Agreement and the Prior Company
Agreement.

     In light of your exceptional services to the Bank and the Company, the
following benefits will be provided upon your retirement from both the Bank and
the Company as of the close of business on December 31, 1996 (or upon your
earlier death):

     1.   The Bank will pay to you (or, in the event of your death, to your
estate) a lump sum payment (to be paid after December 31, 1996, but no later
than March 18, 1997) in the amount of $4,000,000.

     2.   The Bank will cause to remain in effect, for the remainder of your
life and the remainder of the life of your wife (to whom you are married on
December 31, 1996 or the earlier date of your death), all medical and dental
insurance coverage maintained by the Bank or the Company immediately prior to
December 31, 1996 or the earlier date of your death, as long as
<PAGE>

                                                                               2


you (or, after your death, your wife) continue to pay any amounts in respect of
such coverage that you were paying immediately prior to December 31, 1996;
provided however, that (i) any medical coverage may be modified so that Medicare
(or other governmental) coverage is primary, with coverage provided by the Bank
supplementary, to the extent permitted by law, (ii) the Bank may pay you the
cash equivalent of the cost of such coverage, and (iii) such coverage (or cash
equivalent payment) will cease upon your full time equivalent employment by
another employer which provides coverage for you which is no less favorable (in
benefits and duration) than that provided by the Bank; provided, further, that
if such other coverage is provided for a lesser duration than your coverage
provided by the Bank, such Bank coverage will cease during the period the other
coverage is provided by another employer, but will resume after such coverage
provided by another employer ceases.

     3.   Your post-retirement death benefit under the Key Executive Life
Insurance/Death Benefit Plan of the Bank shall be in the amount of $6,480,000,
shall be fully vested, and shall otherwise be payable in accordance with the
terms of that Plan.

     4.   Each vested stock option (including those stock options that vest upon
your death or retirement) relating to common stock of the Company held by you
shall (to the extent permitted by the plan under which it was granted),
notwithstanding anything to the contrary in the grant letter or agreement
related to such vested stock option, remain exercisable by you for the term
specified in such grant letter or agreement as if there had been no termination
of your employment and you remained in the employment of the Bank for the entire
term of the vested stock option.

     5.   Your benefit under the Dime Bancorp, Inc. Supplemental Executive
Retirement Plan (the "SERP") (which shall be calculated without regard to any
payments made in connection with your retirement (or death) hereunder) shall be
fully vested as though you had completed 10 years of service, and will be
determined on the basis of Average Compensation (for purposes of the SERP) of
$900,683.50, or such higher amount as may apply under the terms of the SERP in
light of your continued employment.

     6.   In addition to the benefits specified above, you (or your
beneficiaries) will be provided with all other benefits to which you are
entitled under other benefit plans of the Bank and the Company solely in
accordance with the terms of such plans.

     All payments hereunder shall be subject to applicable tax withholding to
the extent required by law.  The Company shall be jointly and severally liable
with the Bank with respect to any benefits or payments due under this Letter
Agreement to you, and agrees to honor any such obligations that are not
fulfilled by the Bank.
<PAGE>

                                                                               3

     Notwithstanding the foregoing, in the event that, prior to December, 31,
1996,  your employment terminates other than by your death, whether after a
Change in Control of the Bank or the Company, as described in Section 11 of the
Prior Bank Agreement, or otherwise, benefits pursuant to the terms of the Prior
Bank Agreement and the Prior Company Agreement (to the extent relevant) that
would otherwise provide for the payment of benefits in those circumstances,
including Sections 7, 8, and 11 of the Prior Bank Agreement, shall be provided
to you or your spouse, as applicable, in lieu of the benefits provided under
this Letter Agreement; provided, however, that no such benefits shall be payable
should you voluntarily terminate your service with the Bank or the Company prior
to December 31, 1996.  In the event that any benefits are thereby provided after
such a Change in Control of the Bank or the Company, such benefits shall not be
less than the benefits provided under this Letter Agreement.  Except to the
extent expressly provided herein, and except with respect to Sections 11(h), 12,
13, 14(a) and 20 of the Prior Bank Agreement, which shall survive, upon your
retirement on December 31, 1996 (or earlier death), the Prior Bank Agreement and
the Prior Company Agreement will be deemed terminated by your voluntary
retirement (or death), without further notice or action by any party thereto,
and you, your spouse and beneficiaries shall have no further right to payment or
benefits thereunder.

      The failure of either you or the Company or the Bank to at any time
require performance by the other party of a provision of this Letter Agreement
(or the Prior Bank Agreement or Prior Company Agreement, to the extent they
remain in effect) or to resort to a remedy at law or in equity or otherwise
shall in no way affect the right of such party to require full performance or to
resort to such remedy at any time thereafter nor shall a waiver by either party
of the breach of any provision of this Letter Agreement (or the Prior Bank
Agreement or Prior Company Agreement, to the extent they remain in effect) be
taken or held to be a waiver of any subsequent breach of such provision unless
expressly so stated in writing.  Without limiting the generality of the
foregoing, your entering into this Letter Agreement does not, prior to its
becoming fully effective upon your retirement on December 31, 1996 (or prior
death), constitute a waiver of any rights you may have had prior to the date of
this Letter Agreement under the Prior Bank Agreement or the Prior Company
Agreement.  No waiver of any of the provisions of this Letter Agreement (or the
Prior Bank Agreement or Prior Company Agreement, to the extent they remain in
effect) shall be effective unless in writing and signed by the party to be
charged.

     This Letter Agreement shall be governed by the laws of the State of New
York, without regard to conflict of laws principles applied in the State of New
York.  No provision of this Letter Agreement that is held to be unenforceable
shall in any way invalidate any other provisions of this Letter Agreement, all
of which shall remain in full force and effect.  Any dispute or controversy
arising under or in connection with this Letter Agreement may, at your option,
be settled exclusively by arbitration in New York City in accordance with the
rules of the American Arbitration Association then in effect and at the Bank's
expense.  Judgment may be entered on the arbitrator's award in any court having
jurisdiction; provided, however, that you shall be entitled to seek specific
performance in a court of your right to be paid until the date of your
termination of
<PAGE>

                                                                               4

employment during the pendency of any dispute or controversy arising under or in
connection with this Letter Agreement. If any legal action or proceeding is
commenced to enforce or interpret the provisions of this Letter Agreement, the
Prior Bank Agreement or the Prior Company Agreement, or to recover damages for
the breach of any of such agreements, all reasonable fees, disbursements and
court costs paid or incurred by you arising out of or resulting from such action
or proceeding shall be paid or reimbursed to you by the Bank, except if the Bank
or the Company shall be the prevailing party in such action or proceeding.

     You agree that, notwithstanding any other provision of this Letter
Agreement, all of the provisions required to be included in this Letter
Agreement pursuant to 12 C.F.R. 563.39(b) are hereby deemed to be incorporated
by reference and to be a part of this Letter Agreement.  The Bank's obligation
to make payments hereunder will be subject to applicable statutory and
regulatory restrictions.  Without limiting the generality of the foregoing, any
payments made to you pursuant to this Letter Agreement or otherwise are subject
to and conditioned upon their compliance with 12 USC Section 1828(k) and any
regulations promulgated thereunder.

                                    Sincerely yours,

                                    The Dime Savings Bank of New York, FSB


                                    By:   /s/ Ira T. Wender
                                         -----------------------------
                                         Ira T. Wender
                                         Chairman of the Compensation
                                         Committee of the Board of Directors

Agreed and Accepted

/s/ James M. Large, Jr.
--------------------------
James M. Large, Jr.

Date:  8/2/96
      --------

Dime Bancorp, Inc.


By:  /s/ Ira T. Wender and Lawrence J. Toal
     --------------------------------------

Date:  8/2/96
      --------