Amendment to Shareholder Rights Agreement


                  AMENDMENT, dated as of June 22, 1997 (the "Amendment"), to the
Shareholder  Rights  Agreement,  dated as of October 19, 1992 (as  amended,  the
"Rights  Agreement"),  between  North  American  Mortgage  Company,  a  Delaware
corporation  (the  "Company"),  and The Bank of New  York,  a New  York  banking
corporation, as Rights Agent (the "Rights Agent").

                                   WITNESSETH

                  WHEREAS,  on October 19,  1992,  the Board of Directors of the
Company  authorized and declared a dividend  distribution  of one Right for each
share of Common Stock  outstanding  at the close of business on the Record Date,
each Right  representing  the right to purchase one  one-hundredth of a share of
Preferred Stock upon the terms and conditions set forth in the Rights Agreement;
and

                  WHEREAS,  the Rights  remain  issued and  outstanding  and the
Rights Agreement remains in effect with respect thereto; and

                  WHEREAS, no Distribution Date has occurred; and

                  WHEREAS,  the  Company  and Dime  Bancorp,  Inc.,  a  Delaware
corporation  ("Dime"),  and The Dime  Savings  Bank of New York,  FSB, a federal
savings  bank  (the  "Bank"),  have  entered  into  an  Agreement  and  Plan  of
Combination  (the  "Combination  Agreement"),  pursuant  to which the Bank would
acquire  the assets and assume the  liabilities  of the  Company  (or assign the
right to acquire such assets and assume such liabilities to a corporation wholly
owned and controlled by the Bank); and

                  WHEREAS,   in  connection  with  the   anticipated   approval,
execution,  and delivery of the Combination Agreement, the Board of Directors of
the Company  has  approved  this  Amendment  and has  directed  the  appropriate
officers  of the  Company to take all  appropriate  steps to execute and deliver
this Amendment.

                  NOW,  THEREFORE,  in  consideration of the premises and mutual
agreements herein set forth, the parties hereby agree as follows:


(1)      Amendment to Section 1(a)

                  The first paragraph of Section 1(a) of the Rights Agreement is
hereby amended to read in its entirety as follows:

                           "(a) 'Acquiring  Person' shall mean any person who or
                  which,  together with all Affiliates (as hereinafter  defined)
                  and Associates (as hereinafter  defined) of such Person, shall
                  be the  Beneficial  Owner (as  hereinafter  defined) of 15% or
                  more of the shares of Common Stock,  but shall not include (i)
                  the Company, (ii) any

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                  Subsidiary  (as  such  term  is  hereinafter  defined)  of the
                  Company,  (iii)  any  employee  benefit  plan or  compensation
                  arrangement  of the Company or any  Subsidiary of the Company,
                  (iv) any  Person  holding  shares of Common  Stock  organized,
                  appointed or  established  by the Company or any Subsidiary of
                  the Company for or pursuant to the terms of any such  employee
                  benefit  plan or  compensation  arrangement;  or (v) until the
                  termination of the  Combination  Agreement in accordance  with
                  its terms,  Dime,  or any Affiliate or Associate of Dime, as a
                  result of their acquisition of Beneficial  Ownership of shares
                  of  Common  Stock by  reason of the  approval,  execution,  or
                  delivery  of the  Combination  Agreement,  or by reason of the
                  consummation   of   any   transaction   contemplated   by  the
                  Combination  Agreement,  so long as Dime,  or any Affiliate or
                  Associate of Dime, is not the  Beneficial  Owner of any shares
                  of Common Stock other than (w) shares of Common Stock of which
                  Dime, or any Affiliate or Associate of Dime, is or becomes the
                  Beneficial  Owner by reason  of the  approval,  execution,  or
                  delivery  of the  Combination  Agreement,  or by reason of the
                  consummation   of   any   transaction   contemplated   by  the
                  Combination Agreement, (x) shares of Common Stock Beneficially
                  Owned by Dime,  or any  Affiliate or Associate of Dime, on the
                  date hereof,  (y) shares of Common Stock of which Dime, or any
                  Affiliate  or  Associate  of Dime,  inadvertently  becomes the
                  Beneficial  Owner  after the date  hereof,  provided  that the
                  number of such  shares of Common  Stock does not exceed 1/2 of
                  1% of the  shares  of  Common  Stock  outstanding  on the date
                  hereof and that Dime,  or any  Affiliate or Associate of Dime,
                  as the case may be,  divests  such  shares of Common  Stock as
                  soon as practicable after it becomes aware of such acquisition
                  of  Beneficial  Ownership,  and (z)  shares  of  Common  Stock
                  Beneficially Owned or otherwise held by Dime, or any Affiliate
                  or Associate of Dime, in fiduciary capacity or in satisfaction
                  of debts  previously  contracted  in good faith  (the  Persons
                  described  in clauses (i)  through  (v) above are  referred to
                  herein as "Exempt Persons")."

                  (2)      Amendment to Section 1(b)

                  Section 1(b) of the Rights Agreement is hereby amended to read
                  in its entirety as follows:

                           "(b) 'Adverse  Person' shall mean any Person declared
                  to be an  Adverse  Person  by the  Board of  Directors  upon a
                  determination  of the Board of Directors that the criteria set
                  forth in Section 11(a)(ii)(B) apply to such Person,  provided,
                  however,  that the Board of Directors  shall not declare Dime,
                  or any Affiliate or Associate of Dime, to be an Adverse Person
                  (i)  as  a  result  of  the   Combination   Agreement,   their
                  acquisition of Beneficial  Ownership of shares of Common Stock
                  by reason of the  Combination  Agreement,  or by reason of the
                  consummation   of   any   transaction   contemplated   by  the
                  Combination Agreement or (ii) unless the Combination Agreement
                  has been terminated in accordance with its terms."


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                  (3)      Addition of Section 1(z).

                  A new Section 1(z) of the Rights Agreement is inserted, to 
                  read in its entirety as follows:

                           "(z) 'Dime' shall mean Dime Bancorp, Inc., a Delaware
                  corporation, and its successors."

                  (4)      Addition of Section 1(aa).

                  A new Section 1(aa) of the Rights Agreement is inserted, to 
                  read in its entirety as follows:

                           "(aa)   'Combination   Agreement'   shall   mean  the
                  Agreement and Plan Combination,  dated as of June 22, 1997, by
                  and among the Company,  Dime, and The Dime Savings Bank of New
                  York,  FSB, a federal savings bank, as the same may be amended
                  from time to time."

                  (5)      Amendment of Section 7(a).   The first sentence of 
                  Section 7(a) of the Rights Agreement is hereby amended to read
                  in its entirety as follows:

                           "(a) Subject to Section 7(e) hereof,  the  registered
                  holder of any  Rights  Certificate  may  exercise  the  Rights
                  evidenced  thereby  (except as otherwise  provided  herein) in
                  whole or in part at any time after the Distribution  Date upon
                  surrender of the Right Certificate,  with the form of election
                  to purchase  and the  certificate  on the reverse side thereof
                  duly executed, along with a signature guarantee and such other
                  and further  documentation  as the Rights Agent may reasonably
                  request,  to the Rights  Agent at the office or offices of the
                  Rights  Agent  designated  for  such  purpose,  together  with
                  payment of the aggregate  Exercise  Price for the total number
                  of one  one-hundredth  of a share of Preferred Stock (or other
                  securities,  cash or other  assets,  as the case may be) as to
                  which such surrendered Rights are then exercised,  at or prior
                  to the earlier of (i) the close of  business  on December  31,
                  2002 (the 'Final Expiration date'), (ii) the time at which the
                  Rights are  redeemed as  provided in Section 23 hereof,  (iii)
                  the time at which such  Rights are  exchanged  as  provided in
                  Section 24 hereof or (iv) the  effective  time of the business
                  combination  provided for in the  Combination  Agreement  (the
                  earlier if (i), (ii),  (iii) or (iv) being herein  referred to
                  as the 'Expiration Date')."

                  (6)  Effectiveness.  This  Amendment  shall be deemed to be in
force and  effective  immediately  prior to the  execution  and  delivery of the
Combination  Agreement.  Except as amended  hereby,  the Rights  Agreement shall
remain in full force and effect and shall be otherwise unaffected hereby.

                  (7)      Defined Terms.  Unless otherwise defined herein, all 
capitalized terms used but not otherwise defined herein shall have the meanings
assigned them in the Rights Agreement.

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                  (8)  Governing  Law.  This  Amendment  shall be deemed to be a
contract made under the laws of the State of New York and for all purposes shall
be  governed  by and  construed  in  accordance  with  the  laws of  such  State
applicable to contracts made and to be performed entirely within such State.

                  (9) Counterparts. This Amendment may be executed in any number
of counterparts,  each of which shall for all purposes be deemed an original and
all of which shall together constitute but one and the same instrument.

                  IN WITNESS  WHEREOF,  the  parties  hereto  have  caused  this
Amendment to be duly executed as of the day and year first above written.

NORTH AMERICAN MORTGAGE COMPANY

By: /s/MARTIN S. HUGHES
-----------------------
Name: Martin S. Hughes
Title: Executive Vice President


BANK OF NEW YORK, as Rights Agent

By: /s/JAMES N. DIMINO
----------------------
Name: James N. Dimino
Title: Assistant Vice President