<PAGE>
 
                                                                     EXHIBIT 4.4

                               WARRANT AGREEMENT

                                    between

                            GLENDALE FEDERAL BANK, 
                             FEDERAL SAVINGS BANK

                                      and

                     CHEMICAL TRUST COMPANY OF CALIFORNIA,
                               as Warrant Agent

                       Warrants to Purchase Common Stock
--------------------------------------------------------------------------------


                                                     Dated as of August 15, 1993
<PAGE>
 
                               WARRANT AGREEMENT

    AGREEMENT, dated as of August 15, 1993, between GLENDALE FEDERAL BANK,
FEDERAL SAVINGS BANK, a federally chartered stock savings bank (the "Bank"), and
                                                                     ----
CHEMICAL TRUST COMPANY OF CALIFORNIA, as Warrant Agent (the "Warrant Agent").
                                                             -------------

    WHEREAS, pursuant to the Plan of Reorganization entered into among the Bank,
GLENFED, Inc. and Glendale Investment Corporation (the "Reorganization Plan"),
                                                        -------------------
the Bank proposes to conduct several interdependent transactions for the purpose
of increasing the regulatory capital of the Bank; and

    WHEREAS, in connection with the Reorganization Plan, the Bank proposes to
issue and deliver its warrant certificates (the "Warrant Certificates")
                                                 --------------------
evidencing warrants (the "Warrants") to acquire, under certain circumstances, an
                          --------
aggregate of up to approximately 10.85 million shares, subject to adjustment, of
its common stock, par value $1.00 per share (the "Bank Common Stock"), and
                                                  -----------------

    WHEREAS, each such Warrant will entitle the owner of record thereof to
acquire one share of Bank Common Stock, subject to adjustment.

    NOW THEREFORE, in consideration of the foregoing, and for the purpose of
defining the terms and provisions of the Warrants and the respective rights and
obligations thereunder of the Bank and the record holders of the Warrants, the
Bank and the Warrant Agent each hereby agrees as follows:

                                   ARTICLE I

                      ISSUANCE AND EXECUTION OF WARRANTS

    SECTION 1.01 FORM OF WARRANT CERTIFICATES. The text of each Warrant
                 ----------------------------
Certificate (and the related forms of exercise and assignment) shall be
substantially in the form attached hereto as Exhibit A and may have such legends
                                             ---------
and endorsements typed, stamped, printed, lithographed or engraved thereon as
the Bank may deem appropriate and as are not inconsistent with the provisions of
this Agreement, or as may be required to comply with any law or with any rule or
regulation pursuant thereto or with any rule or regulation of any securities
exchange or over-the-counter market on which the Warrants may be listed or
quoted, or to conform to customary usage.
<PAGE>
 
    SECTION 1.02 EXECUTION AND COUNTERSIGNATURE OF WARRANT CERTIFICATES. Warrant
                 ------------------------------------------------------
Certificates shall be executed on behalf of the Bank by its Chief Executive
Officer, President or any Vice President and attested by its Secretary or an
Assistant Secretary, and delivered to the Warrant Agent, and shall be
countersigned and delivered by the Warrant Agent upon the written order of the
Bank signed by any such officer of the Bank. Each Warrant Certificate shall be
dated the date of its countersignature by the Warrant Agent either upon initial
issuance or upon division, exchange, substitution or transfer. Warrant
Certificates shall be executed on behalf of the Bank either manually or by
facsimile signature printed thereon. The Warrant Agent shall countersign the
Warrant Certificate manually, and no Warrant Certificate shall be valid for any
purpose unless so countersigned. In case any officer whose signature has been
placed upon any Warrant Certificate ceases to be such before such Warrant
Certificate is issued, it may be issued with the same effect as if such officer
had not ceased to be such at the date of issuance.

                                  ARTICLE II  

                       EXERCISE PRICE, TERM, REDEMPTION 
                            AND METHOD OF EXERCISE

    SECTION 2.01 EXERCISE PRICE. Each Warrant Certificate shall, when
                 --------------
countersigned by the Warrant Agent, entitle the registered holder thereof (the
"Warrant Holder"), subject to the provisions thereof and of this Agreement, to
 --------------
purchase one share of Bank Common Stock for each Warrant represented thereby at
an exercise price of Twelve Dollars ($12.00) per share in lawful money of the
United States of America (such exercise price per share, as adjusted from time
to time as provided herein, is referred to herein as the "Exercise Price").
                                                          --------------

    SECTION 2.02 WARRANT RIGHTS. Each Warrant shall entitle the Warrant Holder,
                 --------------
upon exercise thereof and payment of the Exercise Price (and any taxes as
contemplated in this Agreement) within the period described in Section 2.03, and
                                                               ------------
subject to the provisions of the Warrant Certificate evidencing such Warrant and
this Agreement, including provisions relating to adjustments upon the occurrence
of certain events as set forth in Article III hereof, to receive one fully paid
                                  -----------
and nonassessable share of Bank Common Stock.

    SECTION 2.03 PERIOD OF EXERCISE; EXPIRATION. Each Warrant may be exercised
                 ------------------------------
on any business day during the period commencing on the day following the first
anniversary of the completion of the Recapitalization (as defined in the
Reorganization Plan) and

                                      -2-
<PAGE>
 
ending at 5:00 pm., New York City time, on the seventh anniversary of the date
of the initial issuance of the Warrants or, if such date is not a business day
in the City of New York, then on the next succeeding business day (the
"Expiration Date"). Each Warrant not exercised by 5:00 p.m., New York City time,
 ---------------
on the Expiration Date shall become void, and all rights thereunder and all
rights in respect thereof under this Agreement shall thereupon cease.

    SECTION 2.04 METHOD OF EXERCISE. Exercise of Warrants shall be effected by:
                 ------------------
(a) surrender of the Warrant Certificate evidencing such Warrants to the Warrant
Agent, with one of the forms on the reverse of or attached to the Warrant
Certificate duly completed and executed by the Warrant Holder thereof or by a
duly appointed legal representative thereof or by a duly authorized attorney
(and with any signatures guaranteed as may be required pursuant to the Warrant
Certificate); and (b) payment of the aggregate Exercise Price for the shares of
Bank Common Stock to which such exercise relates. Warrant Certificates
representing Warrants being exercised (accompanied by payment therefor) shall be
surrendered at the office of the Warrant Agent. In the event that any Warrant
Holder shall exercise less than all of the Warrants evidenced by a Warrant
Certificate surrendered upon exercise of Warrants, a new Warrant Certificate for
the balance of such Warrants shall be countersigned and delivered to, or in
accordance with the instructions of, such Warrant Holder.

    Promptly upon surrender of a Warrant Certificate in conformity with the
foregoing provisions, the Warrant Agent (after requisitioning any certificates
for shares of Bank Common Stock from the Bank's transfer agent, if necessary)
shall deliver to, or in accordance with the instructions of, the Warrant Holder
certificates for the total number of whole shares of Bank Common Stock for which
the Warrants evidenced by such Warrant Certificates are being exercised (subject
to the provisions of Section 4.04) in such names and denominations as the
                     ------------
Warrant Holder has directed; provided, however, that, if, on the date of
                             --------  -------
surrender of such Warrant Certificate, the transfer books for the Bank Common
Stock shall be closed, the certificates for the shares of Bank Common Stock
shall be issuable as of the date on which such books shall next be open (whether
before, on or after the Expiration Date) at the Exercise Price and upon the
other conditions in effect on the date of such surrender.

    SECTION 2.05. DISPOSITION OF PROCEEDS ON EXERCISE OF WARRANTS. The Warrant
                  -----------------------------------------------
Agent shall account promptly to the Bank with respect to Warrants exercised and
concurrently pay to the Bank all moneys received by the Warrant Agent for the
purchase of shares of Bank Common Stock through the exercise of such Warrants.

                                      -3-
<PAGE>
 
    SECTION 2.06. CANCELLATION OF WARRANTS. In the event the Bank shall purchase
                  ------------------------
or otherwise acquire Warrants, the same shall thereupon be delivered to the
Warrant Agent and be cancelled by it and retired. The Warrant Agent shall cancel
any Warrant surrendered for exchange, substitution, transfer or exercise in
whole or in part.

                                  ARTICLE III

                  ADJUSTMENTS TO WARRANTS UPON CERTAIN EVENTS

    SECTION 3.01 ADJUSTMENTS TO WARRANT SHARES OR EXERCISE PRICE. The number of
                 -----------------------------------------------
shares of Bank Common Stock issuable upon the exercise of each Warrant (such
shares being referred to in this Article III as the "Warrant Shares") and the
                                 -----------         --------------
Exercise Price, as applicable, shall be subject to adjustment solely as follows:

    (a) In case the Bank shall at any time after the date of this Agreement (i)
declare a dividend on, or make a distribution with respect to, Bank Common Stock
which is payable in shares of Bank Common Stock, (ii) subdivide the outstanding
shares of Bank Common Stock, (iii) combine the outstanding shares of Bank Common
Stock into a smaller number of shares, or (iv) issue any shares of capital stock
of the Bank in a reclassification of the Bank Common Stock, the number of
Warrant Shares shall be adjusted so that the holder of each Warrant shall be
entitled to receive upon payment of the Exercise Price the aggregate number and
kind of shares of Bank Common Stock or other capital stock of the Bank which, if
such Warrant had been exercised immediately prior to the occurrence of such
event, such holder would have owned or have been entitled to receive immediately
after the occurrence of such event. The time of occurrence of an event giving
rise to an adjustment made pursuant to this Section 3.01(a) shall, in the case
                                            ---------------
of a subdivision, combination or reclassification, be the effective date thereof
and shall, in case of a dividend or distribution, be the record date thereof.

    (b) If at any time after the date hereof, the Bank shall, to or for the
account or benefit of all holders of the outstanding shares of Bank Common
Stock, make, without any charge, any distribution of rights to subscribe or
warrants to purchase Bank Common Stock at a price per share less than the
Current Market Prime (as defined below) of such Bank Common Stock (not
including, in any event, the rights to purchase Bank Common Stock to be issued
pursuant to the Reorganization Plan) on the record date for such distribution or
issuance, the Exercise Price shall be adjusted immediately thereafter so that it
shall equal the price determined in accordance with the following formula:

                                      -4-
<PAGE>
 
                         WP' = WP x A + B(SP/CMP) 
                                    -------------
                                        A + B
 
Where:
         WP'    =     Adjusted Exercise Price;
 
         WP     =     Exercise Price in effect immediately prior to
                      adjustment;
 
         A      =     Number of shares of Bank Common Stock outstanding
                      on the record date for such distribution or
                      issuance;
 
         B      =     Number of shares of Bank Common Stock so offered
                      for subscription or purchase;
 
         SP     =     Subscription or purchase price per share issuable
                      upon exercise of such rights or warrants; and
 
         CMP    =     Current Market Price on the record date for such
                      distribution or issuance.

An adjustment made pursuant to this Section 3.01(b) shall become effective
                                    ---------------
immediately after the record date for the determination of shareholders entitled
to receive such distribution or issuance.

    (c) Upon each adjustment of the number or kind of shares of capital stock
purchasable upon exercise of each Warrant pursuant to Section 3.01(a), the
                                                      ---------------
Exercise Price shall also be adjusted such that upon the exercise of a Warrant
by a Warrant Holder thereafter, and payment of an amount equal to the Exercise
Price immediately prior to such adjustment, such Warrant Holder shall be
entitled to receive the number and kind of such shares of capital stock that
such Warrant Holder would have owned or been entitled to receive immediately
after the occurrence, and as a result, of the event giving rise to such
adjustment had such Warrant been exercised immediately prior to the occurrence
of such event. If, as a result of an adjustment made pursuant to Section
                                                                 -------
3.01(a), a Warrant Holder shall become entitled to receive, upon exercise of its
-------
Warrants and payment therefor, shares of two or more classes of capital stock,
the Board of Directors of the Bank (whose determination with respect to the
matter shall be conclusive and shall be described in a resolution adopted with
respect thereto) shall determine the allocation of the adjusted Exercise Price
between or among shares of such classes of capital stock. After each adjustment
of the Exercise Price pursuant to Section 3.01(b), the total number of Warrant
                                  ---------------

                                      -5-
<PAGE>
 
Shares or fractional part thereof purchasable upon the exercise of each Warrant
shall not be proportionately adjusted.

    (d) Except for adjustments required by Section 3.01(e), no adjustment in the
                                           ---------------
Exercise Price or in the number of Warrant Shares shall be required unless such
adjustment would require an increase or decrease of at least one percent (1%) in
such Exercise Price or in the number of Warrant Shares purchasable; provided,
                                                                    --------
however, that any adjustments which by reason of this Section 3.01(d) are not
-------                                               ---------------
required to be made shall be carried forward and taken into account in any
subsequent adjustment. All calculations under this Section 3.01 shall be made to
                                                   ------------
the nearest cent and to the nearest one-hundredth of a share, as the case may
be.

    (e) In case of any consolidation of the Bank with, or merger of the Bank
into, another corporation or in case of any sale or conveyance to another
corporation or entity of the property of the Bank as an entirety or
substantially as an entirety (such successor or purchaser corporation or entity
being referred to for purposes of this Section 3.01(e) as the "Acquiring
                                       ---------------         ---------
Corporation"), the Bank or the Acquiring Corporation, as the case may be, shall
-----------
execute with the Warrant Agent an agreement that each Warrant Holder shall have
the right, upon exercise of each of its Warrants and payment, prior to 5:00
p.m., New York City time, on the Expiration Date, of the Exercise Price in
effect immediately prior to such consolidation, merger, sale or conveyance, to
purchase upon exercise of such Warrant or Warrants the kind and amount of shares
or other securities or property (including cash) that such holder would have
owned or have been entitled to receive immediately after the happening of such
action, had such Warrant been exercised immediately prior thereto. The Bank
shall mail or cause to be mailed by first-class mail, postage prepaid, to each
Warrant Holder, notice of the execution of any such agreement. Such agreement
shall provide for adjustments, which shall be as nearly equivalent as may be
practicable to the adjustments provided for herein. The provisions of this
Section 3.01(e) shall similarly apply to successive consolidations, mergers,
---------------
sales or conveyances. The Warrant Agent shall be under no responsibility to
determine the correctness of any provisions contained in any such agreement
relating either to the kind or amount of shares or other securities or property
receivable upon exercise of Warrants or with respect to the method employed and
provided therein for any adjustments and shall be entitled to rely upon the
provisions contained in any such agreement.

    (f) Upon the expiration of any rights or warrants pursuant to which an
adjustment in the Exercise Price has been made pursuant to Section 3.01(b)
                                                           ---------------
hereof, if any of such rights or warrants shall not have been exercised, the
Exercise Price in

                                      -6-
<PAGE>
 
effect upon such expiration shall be readjusted in the following manner: (i) the
adjusted Exercise Price determined in respect of the original distribution of
the expired rights or warrants pursuant to Section 3.01(b) hereof (the "Original
                                           ---------------              --------
Adjusted Exercise Price") shall be replaced with a revised Exercise Price (the
-----------------------
"Revised Exercise Price") determined by applying the formula set forth in
 ----------------------
Section 3.01(b) hereof, using the same values for each of the variables in such
---------------
formula as were used in calculating the Original Adjusted Exercise Price, except
that the value for variable "B" shall equal the number of shares of Bank Common
Stock, if any, actually issued or sold upon the exercise of such rights or
warrants, rather than the number of shares of Bank Common Stock offered for
subscription or purchase; and (ii) if any further adjustments shall have been
made to the Original Adjusted Exercise Price pursuant to either Section 3.01(b)
                                                                ---------------
or (c) subsequent to the original distribution of the expired rights or
   ---
warrants, then each such subsequent adjustment shall be recalculated in the same
manner as originally determined, using as a starting point for such subsequent
adjustments the Revised Exercise Price in place of the Original Adjusted
Exercise Price.

    (g) Whenever the Exercise Price or the number of Warrant Shares shall be
adjusted as provided in this Section 3.01, the Bank shall forthwith file with
                             ------------
the Warrant Agent a certificate, signed by the chief financial officer of the
Bank, showing in detail the facts requiring such adjustment and the Exercise
Price and number of Warrant Shares that will be effective after such adjustment.
The Warrant Agent shall have no duty with respect to any certificate filed with
it except to keep the same on file and available for inspection by Warrant
Holders during reasonable business hours. The Warrant Agent shall not at any
time be under any duty or responsibility to any Warrant Holder to determine
whether any facts exist which may require any adjustment of the Exercise Price
or in the number of Warrant Shares, or with respect to the nature of any
adjustment of the Exercise Price or in the number of Warrant Shares purchasable
upon the exercise of each Warrant when made, or with respect to the method
employed in making such adjustment, and shall not be deemed to have knowledge of
any such adjustment unless and until it shall receive such certificate.

    (h) In case the Bank after the date hereof shall propose to take any action
of the type described in this Section 3.01 (except for actions which, pursuant
                              ------------
to Section 3.01(d), would not require an adjustment of the Exercise Price or the
   ---------------
number of Warrant Shares), the Bank shall give notice thereof to the Warrant
Agent by filing with the Warrant Agent a certificate, signed by the Chairman or
Vice Chairman of the Board of Directors, the President or any Vice President of
the Bank and the Bank's Treasurer or any Assistant Treasurer or Secretary or any
Assistant Secretary, specifying the date on which such action

                                      -7-
<PAGE>
 
shall take place, and shall also set forth such facts with respect thereto as
shall be reasonably necessary to indicate the effect of such action (to the
extent such facts may be known on the date of such notice) on the Exercise Price
and the number, kind or class of shares or other securities or property which
shall be purchasable upon exercise of Warrants. The Bank also shall cause a
notice setting forth any such proposed adjustments to be sent by mailing first
class, postage prepaid, to each Warrant Holder as of a date within ten (10) days
of the date of such notice at its address appearing on the Warrant register.
Failure to give such notice or any defect therein shall not affect the legality
or validity of such action. Such notices shall be given, in the case of any
action of the type specified in Sections 3.01(a) and (b), at least ten (10) days
                                ----------------     ---
prior to the effective date or the record date, as applicable, with respect
thereto and in the case of any action of the type specified in Sections 3.01(e)
                                                               ----------------
and (f), at least ten (10) days prior to the taking of such proposed action.
    ---

    (i) Irrespective of any of the adjustments in the Exercise Price or the
number of Warrant Shares, Warrant Certificates shall continue to express on the
face thereof the same price and number of Warrant Shares as stated in a similar
Warrant Certificate issuable initially pursuant to this Agreement and such
number of Warrant Shares and price specified therein shall be deemed to have
been so adjusted.

    (j) For purposes of this Section 3.01, the "Current Market Price" per share
                             ------------       --------------------
of Bank Common Stock on any date shall be deemed to be the arithmetic average of
the Market Price per share of Bank Common Stock (as defined below) for the ten
(10) consecutive Trading Days (as defined below) ending on the Trading Day
immediately preceding the day in question. "Market Price" for each Trading Day
                                            ------------
shall be the closing sale price for the Bank Common Stock on the New York Stock
Exchange, or if no such sale has taken place on such day, then the average of
the closing bid and ask prices for the Bank Common Stock on the New York Stock
Exchange. If the Bank Common Stock hereafter ceases to be listed or admitted for
trading on the New York Stock Exchange, but is listed or admitted for trading on
a national securities exchange, the Market Price shall be the closing price (or
if no such sale has taken place on such day, then the average of the closing bid
and ask prices) on the principal national securities exchange on which the Bank
Common Stock is listed or admitted for trading. If the Bank Common Stock is not,
or hereafter ceases to be, listed or admitted for trading on any national
securities exchange, the Market Price shall be the closing sale price quoted
(or, if no such price is quoted for such day, then the average of the closing
bid and ask prices quoted) for the Bank Common Stock on the NASDAQ National
Market System, or, if the Bank Common Stock is not quoted on such National
Market System, the average

                                      -8-
<PAGE>
 
of the closing bid and ask prices as furnished by any New York Stock Exchange
member firm selected from time to time by the Board of Directors of the Bank for
such purposes (other than the Bank or any affiliate thereof). In the event that
it is impracticable for the Board of Directors of the Bank to establish the
Market Price of the Bank Common Stock as contemplated herein, Market Price shall
mean the fair market value of the Bank Common Stock as determined in good faith
by the Board of Directors of the Bank. "Trading Day" shall be each Monday
                                        -----------
through Friday, other than any day on which securities are not traded in the
system or on the exchange that is the principal market for the Bank Common
Stock, as determined by the Board of Directors of the Bank.

    (k) For the purposes of this Section 3.01, the term "Bank Common Stock"
                                 ------------            -----------------
shall mean (i) the class of capital stock designated as the Common Stock, par
value $1.00 per share, of the Bank, at the date of this Agreement or (ii) any
other class of stock resulting from successive changes or reclassifications of
such capital stock consisting solely of changes in par value, or from par value
to no par value, or from no par value to par value. In the event that at any
time, as a result of an adjustment made pursuant to Section 3.01(a) or (e),
                                                    ---------------    ---
shares of the Bank other than shares of Bank Common Stock are issuable upon
exercise of the Warrants, thereafter the number and Exercise Price of such other
shares so issuable shall be subject to adjustment from time to time in a manner
and on terms as nearly equivalent as practicable to the provisions with respect
to the Bank Common Stock contained in this Section 3.01, as may be determined in
                                           ------------
good faith by the Board of Directors of the Bank, and all other provisions of
this Agreement with respect to Bank Common Stock shall apply on like terms to
any such other shares. Subject to the foregoing, and unless the context requires
otherwise, all references to Bank Common Stock and Warrant Shares in this
Agreement and in the Warrant Certificates shall, in the event of an adjustment
pursuant to this Section 3.01, be deemed to refer also to any other securities
                 ------------
or property then issuable upon exercise of the Warrants as a result of such
adjustment.

   SECTION 3.02 NO ADJUSTMENT FOR CASH DIVIDENDS. No adjustment shall be made in
                --------------------------------
the Exercise Price or in the number of Warrant Shares purchasable upon exercise
of the Warrants in respect of any cash dividends paid or payable on shares of
Bank Common Stock or other securities of the Bank.

                                  ARTICLE IV

                           RIGHTS OF WARRANT HOLDERS

                                      -9-
<PAGE>
 
    SECTION 4.01 NO RIGHTS AS STOCKHOLDERS. No Warrant Holder, as such, shall be
                 -------------------------
entitled to vote or to receive dividends or shall otherwise be deemed to be the
holder of shares of Bank Common Stock for any purpose, nor shall anything
contained herein or in any Warrant Certificate be construed to confer upon any
Warrant Holder, as such, any of the rights of a stockholder of the Bank or any
right to vote upon or give or withhold consent to any action of the Bank
(whether upon any reorganization, issuance of securities, reclassification or
conversion of Bank Common Stock, consolidation, merger, sale, lease, conveyance
or otherwise), receive notice of meetings or other action affecting stockholders
(except for notices expressly provided for in this Agreement) or receive
dividends or subscription rights, unless and until such Warrant Certificate
shall have been surrendered for exercise as provided in this Agreement, payment
in respect of such exercise shall have been received by the Warrant Agent, and
shares of Bank Common Stock thereunder shall have become issuable and such
person shall have been deemed to have become a holder of record of such shares.
If, at the date of surrender of such Warrant Certificate, the transfer books for
the Bank Common Stock shall be closed, certificates for the shares of Bank
Common Stock shall be issuable on the date on which such books shall next be
open (whether before, on or after the Expiration Date) and, until such date, the
Bank shall be under no duty to deliver any certificate for such shares of Bank
Common Stock. No Warrant Holder shall, upon the exercise of Warrants, be
entitled to any dividends if the record date with respect to payment of such
dividends shall be a date prior to the date such shares of Bank Common Stock
became issuable upon the exercise of such Warrants.

    SECTION 4.02 LOST WARRANTS. If any Warrant Certificate is lost, stolen,
                 -------------
mutilated or destroyed, the Warrant Agent may, upon receipt of evidence
satisfactory to the Bank and the Warrant Agent of such loss, theft, mutilation
or destruction and on such terms as to indemnity or otherwise as the Bank and
the Warrant Agent may in their discretion require (which shall, in the case of a
mutilated Warrant Certificate, include the surrender thereof), issue a new
Warrant Certificate of like denomination and tenor as the lost, stolen,
mutilated or destroyed Certificate, and the Warrant Agent shall countersign and
deliver such new Certificate. Applicants for such substitute Warrant
Certificates shall also comply with such other reasonable regulations and pay
any such reasonable charges as the Bank or the Warrant Agent may prescribe. In
the event any Warrant Certificate is lost, stolen, mutilated or destroyed, and
the owner thereof desires to exercise the Warrants evidenced thereby, the Bank
may, in lieu of issuing a substitute Warrant Certificate, authorize the exercise
thereof upon receipt of the above evidence and on such terms of indemnity as it
may require.

                                      -10-
<PAGE>
 
   SECTION 4.03 MAINTENANCE OF SUFFICIENT AND PROPER SHARES OF BANK COMMON
                ----------------------------------------------------------
STOCK; LISTING; CONTINUING REGISTRATION.
---------------------------------------

    (a) The Bank shall at all times reserve and keep available a number of
authorized shares of Bank Common Stock (and any other securities that may become
issuable upon the exercise of Warrants) sufficient to permit the exercise in
full of all outstanding Warrants and will cause to be available to the Warrant
Agent a sufficient number of certificates therefor. The transfer agent for the
Bank Common Stock is hereby irrevocably authorized and directed at all times to
reserve such number of authorized shares of Bank Common Stock (or other
securities) for such purpose. The Warrant Agent is hereby irrevocably authorized
to requisition from time to time from such transfer agent certificates for
shares of Bank Common Stock issuable upon exercise of outstanding Warrants and
the Bank shall supply such transfer agent with duly executed certificates for
such purpose.

    (b) The Bank covenants and agrees that it will use its best efforts to
secure the listing of shares of Bank Common Stock issuable upon the exercise of
the Warrants upon any and all securities exchanges on which the Bank Common
Stock shall be listed at the dates of exercise of such Warrants.

    (c) So long as any unexpired Warrants remain outstanding and to the extent
required in order to comply with the applicable regulations of the Office of
Thrift Supervision (the "OTS Rules"), the Bank covenants and agrees to file such
                         ---------
post-effective amendments to the offering circular filed with respect to the
Warrants under cover of Form OC pursuant to the OTS Rules (OTS No. 3088), or
such other offering circulars, post-effective amendments or supplements, as may
be necessary to permit the Bank to offer and sell in accordance with the OTS
Rules shares of Bank Common Stock upon the exercise of Warrants pursuant to this
Agreement. The Bank further covenants and agrees that, so long as any unexpired
Warrants remain outstanding, it shall exercise its reasonable diligence to
obtain and keep effective any other permits, consents and approvals of other
governmental authorities, and to qualify the shares of Bank Common Stock
issuable upon the exercise of Warrants, and maintain such qualification, under
the securities laws of such of the States of the United States, as may be
necessary to permit the offer and sale of shares of Bank Common Stock upon the
exercise of Warrants pursuant to this Agreement. The Bank shall not be required
to issue any shares of Bank Common Stock pursuant to the exercise of Warrants
for any period during which the Bank is endeavoring to obtain such continuing
registration, permits, consents, approvals or qualifications.

SECTION 4.04 FRACTIONAL SHARES AND WARRANTS.
             ------------------------------

                                      -11-
<PAGE>
 
    (a) Anything contained herein to the contrary notwithstanding, the Bank
shall not be required to issue any fraction of a share of Bank Common Stock in
connection with the exercise of Warrants. Warrants may not be exercised in such
number as would result (except for the provisions of this Section) in the
issuance of a fraction of a share of Bank Common Stock unless the Warrant Holder
is presenting for exercise Warrant Certificates representing all Warrants then
owned of record by such Warrant Holder. In such event, the Bank shall, upon the
exercise of all of such Warrants, issue to such Warrant Holder the aggregate
number of shares of Bank Common Stock called for thereby, rounded to the nearest
whole number of shares.

    (b) Anything herein to the contrary notwithstanding, the Bank shall not be
required to issue fractions of Warrants on any distribution of Warrants to
Warrant Holders or to distribute Warrant Certificates that evidence fractional
Warrants. In such event, the Bank shall issue to such Warrant Holders the
aggregate number of Warrants to which such Warrant Holders are entitled, in each
case rounded to the nearest whole Warrant.

   SECTION 4.05 TRANSFER AND EXCHANGE OF WARRANTS. The Warrant Certificates
                ---------------------------------
shall be issued in registered form only. The Bank shall cause to be kept at the
office of the Warrant Agent a register in which, subject to such reasonable
regulations as the Warrant Agent may prescribe, the Bank shall provide for the
registration of Warrant Certificates and of transfers or exchanges of Warrant
Certificates as herein provided.

   At the option of the Warrant Holder, Warrant Certificates may be exchanged at
such office, and upon payment of the charges hereinafter provided. Whenever any
Warrant Certificates are so surrendered for exchange, the Bank shall execute,
and the Warrant Agent shall countersign and deliver, the Warrant Certificates
that the Warrant Holder making the exchange is entitled to receive.

   All Warrant Certificates issued upon any registration of transfer or exchange
of Warrant Certificates shall be the valid obligations of the Bank, evidencing
the same obligations, and entitled to the same benefits under this Agreement, as
the Warrant Certificates surrendered for such registration of transfer or
exchange.

   Every Warrant Certificate surrendered for registration of transfer or
exchange shall (if so required by the Bank or the Warrant Agent) be duly
endorsed, or be accompanied by a written instrument of transfer in form
satisfactory to the Bank and the Warrant Agent, duly executed by the Warrant
Holder thereof by a duly appointed legal representative or by a duly authorized

                                      -12-
<PAGE>
 
attorney (and with any signatures guaranteed as may be required pursuant to the
Warrant Certificate).

    No service charge shall be made by the Warrant Agent for any registration of
transfer or exchange of Warrant Certificates. The Bank may require payment of a
sum sufficient to cover certain taxes or other governmental charges as provided
in Section 6.03.
   ------------

   Any Warrant Certificate when duly endorsed in blank shall be deemed
negotiable and when a Warrant Certificate shall have been so endorsed, the
holder thereof may be treated by the Bank, the Warrant Agent and all other
persons dealing therewith as the absolute owner thereof for any purpose and as
the person entitled to exercise the rights represented thereby, or to the
transfer thereof on the register of the Bank maintained by the Warrant Agent,
any notice to the contrary notwithstanding; but until such transfer on such
register, the Bank and the Warrant Agent may treat the Warrant Holder thereof as
the owner for all purposes.

                                  ARTICLE V 

                                 WARRANT AGENT

   SECTION 5.01 NATURE OF DUTIES AND RESPONSIBILITIES ASSUMED. The Bank hereby
                ---------------------------------------------
appoints the Warrant Agent to act as agent of the Bank as set forth in this
Agreement. The Warrant Agent hereby accepts the appointment as agent of the Bank
and agrees to perform that agency upon the terms and conditions herein set
forth, by all of which the Bank and the Warrant Holders, by their acceptance of
the Warrants, shall be bound.

   Whenever in the performance of its duties under this Agreement, the Warrant
Agent shall deem it necessary or desirable that any fact or matter be proved or
established by the Bank prior to taking or suffering any action hereunder, such
fact or matter (unless other evidence in respect thereof be herein specifically
prescribed) may be deemed to be conclusively proved and established by a
certificate signed by the Chief Executive Officer, the President, any Vice
President or the Secretary of the Bank and delivered to the Warrant Agent; and
such certificate shall be full authorization to the Warrant Agent for any action
taken or suffered in good faith by it under the provisions of this Agreement in
reliance upon such certificate.

   The Warrant Agent shall be liable hereunder only for its own negligence, bad
faith or willful misconduct. The Warrant Agent shall not be liable for or by
reason of any of the statements of fact or recitals contained in this Agreement
or in the Warrant Certificates (except its countersignature on the Warrant

                                      -13-
<PAGE>
 
Certificates and such statements or recitals as describe the Warrant Agent or
action taken or to be taken by it) or be required to verify the same, but all
such statements and recitals are and shall be deemed to have been made by the
Bank only. The Warrant Agent shall not have any liability or responsibility in
respect of the legality, validity or enforceability of this Agreement or the
execution and delivery hereof (except the due execution hereof by the Warrant
Agent) or in respect of the validity or execution of any Warrant Certificate
(except its countersignature thereof); nor shall it be responsible or liable for
any breach by the Bank of any covenant or condition contained in this Agreement
or in any Warrant Certificate; nor shall it be responsible or liable for the
making of any change in the number of shares of Bank Common Stock required under
the provisions of Article III or responsible for the manner, method or amount of
                  -----------
any such change or the ascertaining of the existence of any facts that would
require any such adjustment or change; nor shall it by any act hereunder be
deemed to make any representation or warranty as to the authorization or
reservation of any shares of Bank Common Stock to be issued pursuant to this
Agreement or any Warrant Certificate or as to whether any shares of Bank Common
Stock will, when issued, be validly issued, fully paid and nonassessable.

    The Warrant Agent shall be under no obligation to institute any action, suit
or legal proceeding or take any other action likely to involve expense unless
the Bank or one or more Warrant Holders shall furnish the Warrant Agent with
reasonable security and indemnity for any costs and expenses which may be
incurred. All rights of action under this Agreement or under any of the Warrants
may be enforced by the Warrant Agent without the possession of any of the
Warrants or the production thereof at any trial or other proceeding relative
thereto, and any such action, suit or proceeding instituted by the Warrant Agent
shall be brought in its name as Warrant Agent, and any recovery of judgment
shall be for the ratable benefit of the Warrant Holders, as their respective
rights or interests may appear. The Warrant Agent shall promptly notify the Bank
in writing of any claim made or action, suit or proceeding instituted against it
arising out of or in connection with this Agreement.

   The Warrant Agent is hereby authorized and directed to accept written
instructions with respect to the performance of its duties hereunder from the
Chief Executive Officer, the President, any Vice President or the Secretary of
the Bank, and to apply to any such officer for advice or instructions in
connection with the Warrant Agent's duties, and it shall not be liable for any
action taken or suffered to be taken or omitted by it in good faith in
accordance with the instructions of any such officer.

                                      -14-
<PAGE>
 
   The Warrant Agent will not be responsible or liable for any failure of the
Bank to comply with any of the covenants contained in this Agreement or in the
Warrant Certificates to be complied with by the Bank. The Warrant Agent will not
incur any liability or responsibility to the Bank or to any Warrant Holder for
any action taken, or any failure to take action, in reliance on any notice,
resolution, waiver, consent, order, certificate, or other paper, document or
instrument reasonably believed by the Warrant Agent to be genuine and to have
been signed, sent or presented by the proper party or parties.

   The Warrant Agent may execute and exercise any of the rights and powers
hereby vested in it or perform any duty hereunder either itself or by or through
its attorneys, agents or employees, provided reasonable care has been exercised
in the selection and in the continued employment of any such attorney, agent or
employee.

   The Bank will perform, execute, acknowledge and deliver or cause to be
performed, executed, acknowledged and delivered all such further acts,
instruments and assurances as may reasonably be required by the Warrant Agent in
order to enable it to carry out or perform its duties under this Agreement.

   The Warrant Agent will act hereunder solely as agent of the Bank in a
ministerial capacity, and its duties will be determined solely by the provisions
hereof. The Warrant Agent will not be liable for anything which it may do or
refrain from doing in connection with this Agreement except for its own
negligence, bad faith or willful misconduct.

   Anything in this Agreement to the contrary notwithstanding, in no event shall
the Warrant Agent be liable for special, indirect or consequential loss or
damage of any kind whatsoever (including but not limited to lost profits), even
if the Warrant Agent has been advised of the likelihood of such loss or damage
and regardless of the form of action.

    SECTION 5.02 RIGHT TO CONSULT COUNSEL. The Warrant Agent may at any time
                 ------------------------
consult with legal counsel satisfactory to it (who may be legal counsel for the
Bank), and the opinion of such counsel shall be full and complete authorization
and protection to the Warrant Agent as to any action taken, suffered or omitted
by it in good faith in accordance with such opinion; provided, however, that the
                                                     --------  -------
Warrant Agent shall have exercised reasonable care in the selection of such
counsel.

    SECTION 5.03 COMPENSATION AND REIMBURSEMENT. The Bank agrees to pay to the
                 ------------------------------
Warrant Agent from time to time compensation for all services rendered by it
hereunder as the Bank and the Warrant Agent may agree from time to time, and to
reimburse the

                                      -15-
<PAGE>
 
Warrant Agent for reasonable expenses and disbursements incurred in connection
with the execution and administration of this Agreement (including the
reasonable compensation and the expenses of its counsel), and further agrees to
indemnify the Warrant Agent for, and to hold it harmless against, any loss,
liability or expense incurred without negligence, bad faith or willful
misconduct on its part, arising out of or in connection with the acceptance and
administration of this Agreement, including the costs and expenses of defending
itself against any claim or liability in connection with the exercise or
performance of any of its powers or duties hereunder.

   SECTION 5.04 WARRANT AGENT MAY HOLD BANK SECURITIES. The Warrant Agent and
                --------------------------------------
any stockholder, director, officer or employee of the Warrant Agent may buy,
sell or deal in any of the Warrants or other securities of the Bank or its
affiliates or have a pecuniary interest in any transaction in which the Bank or
its affiliates may be interested, or contract with or lend money to the Bank or
its affiliates or otherwise act as fully and freely as though it were not the
Warrant Agent under this Agreement. Nothing herein shall preclude the Warrant
Agent from acting in any other capacity for the Bank or for any other legal
entity.

    SECTION 5.05 CHANGE OF WARRANT AGENT. The Warrant Agent may resign and be
                 -----------------------
discharged from its duties under this Agreement upon 60 days' prior notice in
writing mailed, by registered or certified mail, to the Bank. The Bank may
remove the Warrant Agent upon 60 days' prior notice in writing, mailed to the
Warrant Agent by registered or certified mail. If the Warrant Agent shall resign
or be removed or shall otherwise become incapable of acting, the Bank shall
appoint a successor to the Warrant Agent (the "Successor Warrant Agent") and
                                               -----------------------
shall, within 30 days following such appointment, give notice thereof in writing
to each Warrant Holder. If the Bank shall fail to make such appointment within a
period of 30 days after giving notice of such removal or after it has been
notified in writing of such resignation or incapacity by the resigning or
incapacitated Warrant Agent, then the Bank agrees to perform the duties of the
Warrant Agent hereunder until the Successor Warrant Agent is appointed. After
appointment, the Successor Warrant Agent shall be vested with the same powers,
rights, duties and responsibilities as if it had been originally named as
Warrant Agent without further act or deed; but the Warrant Agent shall deliver
and transfer to the Successor Warrant Agent any property at the time held by it
hereunder, and execute and deliver any further assurance, conveyance, act or
deed necessary for the purpose. Failure to give any notice provided for in this
Section, however, or any defect therein shall not affect the legality or
validity of the resignation or removal of the Warrant Agent or the appointment
of the Successor Warrant Agent, as the case may be.

                                      -16-
<PAGE>
 
                                  ARTICLE VI 

                                    GENERAL

    SECTION 6.01 PURCHASE OF WARRANTS BY THE BANK. The Bank shall have the
                 --------------------------------
right, except as limited by law or other agreement, to purchase or otherwise
acquire Warrants at such times, in such manner and for such consideration as it
may deem appropriate.

   SECTION 6.02 CANCELLED WARRANTS. The Warrant Agent shall cancel any Warrant
                ------------------
Certificate delivered to it for exercise, in whole or in part, or delivered to
it for transfer, or for splitup, combination, exchange or substitution and shall
deliver to the Bank, in a manner satisfactory to the Bank, such cancelled
Warrant Certificates.

   SECTION 6.03 TAXES ON ISSUANCE OF SHARES OF BANK COMMON STOCK. The Bank shall
                ------------------------------------------------
from time to time promptly pay all documentary stamp taxes, if any, that may be
imposed upon the Bank or the Warrant Agent with respect to the initial issuance
of Warrants and of shares of Bank Common Stock upon the exercise of Warrants,
provided, however, that the Bank shall not be required to pay any tax or taxes
--------  -------
that may be payable in respect of any transfer involved in the issue of any
Warrant Certificates or any certificates for shares of Bank Common Stock in a
name other than that of the Warrant Holder of the Warrant Certificate
surrendered upon the exercise of Warrants, and the Bank shall not be required to
issue or deliver such certificates unless and until the person or persons
requesting issuance thereof shall have paid to the Bank the amount of such tax
or shall have established to the satisfaction of the Bank that such tax has been
paid.

   SECTION 6.04 DATES AND TIMES. If any date set forth in this Warrant Agreement
                ---------------
shall fall on a day other than a full business day in New York City, said date
shall be deemed to be the next full business day succeeding that date. All times
shall be the legal time then in effect in New York City.

    SECTION 6.05 AMENDMENTS TO WARRANT AGREEMENT. The Bank and the Warrant Agent
                 -------------------------------
may, jointly, without the consent or concurrence of the Warrant Holders, by
supplemental agreement or otherwise, make any amendments, alterations, deletions
or corrections in this Agreement that they deem necessary or desirable: (a) to
cure any ambiguity or correct any defect, inconsistency, clerical omission or
mistake, or manifest error contained herein; (b) to confer additional rights
upon the Warrant Holders; or (c) in any other respect that is not

                                      -17-
<PAGE>
 
inconsistent with the provisions of the Warrants and which does not adversely
affect the interests of the Warrant Holders hereunder. The Bank and the Warrant
Agent also may supplement or amend the Warrant Agreement in any other respect
without notice to any Warrant Holder but with the written consent of the holders
of more than 50% in number of the Warrants then outstanding; provided, however,
                                                             --------  -------
that no such supplement or amendment may (i) make any modification of the terms
upon which the Warrants are exercisable or (ii) change the percentage of the
holders of the Warrants who must consent to such amendment or supplement,
without the consent of each Warrant Holder affected thereby.

   SECTION 6.06 BINDING AGREEMENTS. All of the covenants and provisions of this
                ------------------
Agreement by or for the benefit of the Bank or the Warrant Agent shall bind and
inure to the benefit of their respective successors and assigns hereunder.
Nothing expressed in this Agreement and nothing that may be implied from any of
the provisions hereof is intended, or shall be construed, to confer upon or give
to any person or corporation, other than the Bank, the Warrant Agent and the
Warrant Holders, any legal or equitable right, remedy or claim under or by
reason of this Agreement or of any covenant, condition, stipulation, promise or
agreement herein, and all covenants, conditions, stipulations, promises and
agreements contained in this Agreement shall be for the sole and exclusive
benefit of the Bank, the Warrant Agent, the Warrant Holders, and their
respective successors and assigns.

   SECTION 6.07 COPIES OF AGREEMENT WITH WARRANT AGENT. A copy of this
                --------------------------------------
Agreement, as such may be amended from time to time, shall be available for
inspection by any Warrant Holder at the office of the Warrant Agent, as
designated in Section 6.08, during normal business hours. As a condition of such
              ------------
inspection, the Warrant Agent may require any such Warrant Holder to submit his
or her Warrant Certificate for inspection.

   SECTION 6.08 NOTICES. Any communication, notice or demand to be given
                -------
hereunder shall be duly given if in writing and delivered, or sent by first
class mail, certified or registered, postage prepaid and addressed as follows:

    (a) If to the Bank:

        Glendale Federal Bank, FSB 
        700 N. Brand Boulevard 
        Glendale, California 91203
        Attention: Secretary

                                      -18-
<PAGE>
 
    (b) If to the Warrant Agent:

        Chemical Trust Company of California 
        300 South Grand Avenue, 2nd Floor 
        Los Angeles, California 90071 
        Attention: Office Manager

    (c) If to a Warrant Holder, at such person's last known address as such
shall appear on the registration books maintained by the Warrant Agent.

    Any party may change the address to which any communications, notice or
demand shall be given by giving notice of such change in conformity with the
provisions of this Section.

    SECTION 6.09 GOVERNING LAW. This Agreement and each Warrant issued hereunder
                 -------------
shall be governed by and construed in accordance with the laws of the State of
California, without giving effect to conflict of laws.

    SECTION 6.10 HEADINGS. The Article and Section headings herein are for
                 --------
convenience only and are not part of this Agreement and shall not affect the
interpretation thereof.

   SECTION 6.11 COUNTERPARTS. This Agreement may be executed in any number of
                ------------
counterparts, each of which so executed shall be deemed to be an original, and
all such counterparts shall together constitute but one and the same instrument.

                                      -19-
<PAGE>
 
    IN WITNESS WHEREOF, this Agreement has been duly executed by the parties
hereto as of the day and year first above written.

                                GLENDALE FEDERAL BANK,
                                  FEDERAL SAVINGS BANK

                                By: /s/ Richard A. Fink
                                    --------------------------------------------
                                    Name:       Richard A. Fink
                                    Title:      Senior Executive Vice
                                                President and Chief Legal
                                                Officer

Attest:

/s/ James R. Eller, Jr.
-----------------------
Secretary

                                CHEMICAL TRUST COMPANY OF CALIFORNIA 
                                  As Warrant Agent

                                By: /s/ Sharon Magidson
                                    --------------------------------------------
                                    Name: Sharon Magidson 
                                    Title: Vice President

Attest:

/s/ Michael Dzieciclowski
-------------------------
Assistant Vice President

                                      -20-
<PAGE>
 
                                                                       EXHIBIT A

                     [FORM OF FACE OF WARRANT CERTIFICATE]

         VOID AFTER 5:00 P.M., NEW YORK CITY TIME, ON AUGUST 21, 2000

        NO.

                  ____________ WARRANT(S) TO PURCHASE SHARES 
                             OF BANK COMMON STOCK

                 GLENDALE FEDERAL BANK, FEDERAL SAVINGS BANK 
                     WARRANT TO PURCHASE BANK COMMON STOCK

   THIS WARRANT CERTIFICATE CERTIFIES that _____________________________________
____________________________________, or registered assigns, is the registered
holder of the number of warrants (the "Warrants") of Glendale Federal Bank,
Federal Savings Bank (the "Bank") set forth above. Each Warrant entitles the
registered holder thereof to purchase one fully paid and nonassessable share of
the Common Stock, par value $1.00 per share (the "Bank Common Stock"), of the
Bank at the exercise price (as may be adjusted as provided in the Warrant
Agreement referred to on the reverse hereof, the "Exercise Price") of $12.00 per
share, in lawful money of the United States of America. The Warrants expire at
5:00 p.m., New York City time, on August 21, 2000 (the "Expiration Date").
Subject to the terms and conditions set forth herein and in the Warrant
Agreement, the Warrants evidenced hereby may be exercised upon surrender of this
Warrant Certificate and payment of the aggregate Exercise Price at the office or
agency of the Warrant Agent in Los Angeles, San Francisco or in the city of New
York (each such office, a "Warrant Agent Office"), on any business day during
the period commencing on the first day following the first anniversary of the
completion of the Recapitalization referred to in the Warrant Agreement and
ending at 5:00 p.m., New York City time, on the Expiration Date.

   The Exercise Price and the number of shares of Bank Common Stock purchasable
upon exercise of the Warrants are subject to adjustment upon the occurrence of
certain events as set forth in the Warrant Agreement.

   NO WARRANT MAY BE EXERCISED AFTER 5:00 P.M., NEW YORK CITY TIME, ON THE
EXPIRATION DATE. AFTER SUCH TIME, THE WARRANTS WILL BECOME WHOLLY VOID AND OF NO
VALUE.

<PAGE>
 
                                     A - 2

   REFERENCE HEREBY IS MADE TO THE FURTHER PROVISIONS OF THIS WARRANT
CERTIFICATE SET FORTH ON THE REVERSE HEREOF. SUCH FURTHER PROVISIONS SHALL FOR
ALL PURPOSES HAVE THE SAME EFFECT AS THOUGH FULLY SET FORTH AT THIS PLACE.

    This Warrant Certificate shall not be valid unless countersigned by the
Warrant Agent.

   IN WITNESS WHEREOF, the Bank has caused this Warrant Certificate to be
executed by its duly authorized officers, and the corporate seal hereunto
affixed.

Dated:

                                                  GLENDALE FEDERAL BANK, FEDERAL
                                                    SAVINGS BANK

[Corporate Seal]                                  By: __________________________

Attest:

By: _________________________________

Countersigned:

CHEMICAL TRUST COMPANY OF CALIFORNIA, 
  as Warrant Agent

By: _________________________________

<PAGE>
 
                                    A - 3 

                   [FORM OF REVERSE OF WARRANT CERTIFICATE] 

                  GLENDALE FEDERAL BANK, FEDERAL SAVINGS BANK

    The Warrants evidenced by this Warrant Certificate is a part of a duly
authorized issue of Warrants to purchase a maximum of up to approximately 10.85
million shares of Bank Common Stock issued pursuant to a Warrant Agreement,
dated as of August 15, 1993 (the "Warrant Agreement"), duly executed and
delivered by the Bank to Chemical Trust Company of California, as Warrant Agent
(the "Warrant Agent"). The Warrant Agreement hereby is incorporated by reference
in and made a part of this instrument and is hereby referred to for a
description of the rights, limitation of rights, obligations, duties and
immunities thereunder of the Warrant Agent, the Bank and the holders (the words
"holders" or "holder" meaning the registered holders or registered holder) of
the Warrants. A copy of the Warrant Agreement may be inspected at the Warrant
Agent Office in Los Angeles and is available upon written request addressed to
the Bank. All terms used herein that are defined in the Warrant Agreement have
the meanings assigned to them therein.

   Warrants may be exercised to purchase shares of Bank Common Stock on any
business day during the period commencing on the first day following the first
anniversary of the completion of the Recapitalization referred to in the Warrant
Agreement and ending at 5:00 p.m., New York City time, on the Expiration Date,
at the Exercise Price set forth on the face hereof, subject to adjustment as
described in the Warrant Agreement. The holder of the Warrants evidenced by this
Warrant Certificate may exercise such Warrants by surrendering the Warrant
Certificate, with the form of election to purchase set forth hereon properly
completed and executed, together with payment of the aggregate Exercise Price,
in lawful money of the United States of America, and any applicable transfer
taxes, at the Warrant Agent Office.

    In the event that less than all of the Warrants evidenced hereby are
exercised, there shall be issued to the holder hereof, or such holder's
assignee, a new Warrant Certificate evidencing Warrants not so exercised. No
adjustment shall be made for any cash dividends on any shares of Bank Common
Stock issuable upon exercise of the Warrants. After 5:00 p.m., New York City
time, on the Expiration Date, unexercised Warrants shall become wholly void and
of no value.

    The Bank shall not be required to issue fractions of shares of Bank Common
Stock or any certificates that evidence fractional shares of Bank Common Stock.
Except as provided in the Warrant Agreement, Warrants may not be exercised in
such number as would

<PAGE>
 
                                     A - 4

result in the issuance of a fraction of a share of Bank Common Stock.

    Warrant Certificates, when surrendered at the Warrant Agent Office by the
registered holder thereof in person or by a legal representative or attorney
duly authorized in writing, may be exchanged, in the manner and subject to the
limitations provided in the Warrant Agreement, but without payment of any
service charge, for another Warrant Certificate or Warrant Certificates of like
tenor evidencing in the aggregate a like number of Warrants.

   Upon due presentment for registration of transfer of this Warrant Certificate
at the Warrant Agent Office, a new Warrant Certificate or Warrant Certificates
of like tenor and evidencing in the aggregate a like number of Warrants shall be
issued to the transferee in exchange for this Warrant Certificate, subject to
the limitations provided in the Warrant Agreement, without charge, except for
any tax or other governmental charge imposed in connection therewith.

   The Bank and Warrant Agent may deem and treat the registered holder hereof as
the absolute owner of this Warrant Certificate (notwithstanding any notation of
ownership or other writing hereon made by anyone) for the purpose of any
exercise hereof and for all other purposes, and neither the Bank nor the Warrant
Agent shall be affected by any notice to the contrary.

<PAGE>
 
                                     A - 5

                             ELECTION TO EXERCISE 

                  (To be executed upon exercise of Warrants)

The undersigned hereby irrevocably elects to exercise _________ Warrants to
purchase shares of Bank Common Stock and herewith tenders in payment for such
shares of Bank Common Stock $_________ in lawful money of the United States of
America, in accordance with the terms hereof. The undersigned requests that a
certificate representing the shares of Bank Common Stock be registered and
delivered as follows:

                Name:                   ________________________________________

                Address:                ________________________________________
                        
                                        ________________________________________

                Delivery Address:       ________________________________________
                 (if different)
                                        ________________________________________

If such number of Warrants is less than the aggregate number of Warrants
represented by this Warrant Certificate, the undersigned requests that a new
Warrant Certificate representing the balance of such shares of Bank Common Stock
be registered and delivered as follows:

                Name:                   ________________________________________

                Address:                ________________________________________
                        
                                        ________________________________________

                Delivery Address:       ________________________________________
                 (if different)
                                        ________________________________________


--------------------------------
(Insert social security or other        Signature: _____________________________
identifying number of holder)

NOTE:   The above signature must correspond with the name as written upon the
        face of this Warrant Certificate in every particular, without alteration
        or enlargement or any change whatsoever. If the certificate representing
        the shares of Bank Common Stock or any Warrant

<PAGE>
 
                                     A - 6

        Certificate representing Warrants not exercised is to be registered in a
        name other than that in which this Warrant Certificate is registered,
        the signature of the holder hereof must be guaranteed by an eligible
        guarantor institution pursuant to SEC Rule 17Ad-15.

SIGNATURE GUARANTEED:


_____________________________

<PAGE>
 
                                    A - 7 

                                  ASSIGNMENT

                      (TO BE EXECUTED BY THE REGISTERED 
                       HOLDER IF SUCH HOLDER DESIRES TO 
                       TRANSFER THE WARRANT CERTIFICATE)

   FOR VALUE RECEIVED, the undersigned registered holder hereby sells, assigns
and transfers unto

________________________________________________________________________________

________________________________________________________________________________
                  (Please print name and address of assignee)

this Warrant Certificate, together with all right, title and interest therein,
and does irrevocably constitute and appoint ____________________________________
_________________________ attorney, to transfer the within Warrant Certificate
on the books of the Warrant Agent, with full power of substitution.

Dated: ___________________________  Signature: _________________________________


__________________________________
(Insert social security or other 
identifying number of assignee)

NOTE:   The above signature must correspond with the name as written upon the
        face of this Warrant Certificate in every particular, without alteration
        or enlargement or any change whatsoever and must be guaranteed by an
        eligible guarantor institution pursuant to SEC Rule 17Ad-15.

SIGNATURE GUARANTEED:

__________________________________

<PAGE>
 
                     AMENDMENT NO. 1 TO WARRANT AGREEMENT

   THIS AMENDMENT NO. 1 TO WARRANT AGREEMENT (this "Amendment No. 1") dated as
of July 24, 1997 is entered into by and among Glendale Federal Bank, Federal
Savings Bank (the "Bank"), ChaseMellon Shareholder Services, LLC (as successor
to Chemical Trust Company of California ("Chemical"), the "Warrant Agent"), and
Golden State Bancorp Inc. ("Golden State") on the basis of the following facts:

   WHEREAS, the Bank and Chemical entered into that certain Warrant Agreement
(the "Warrant Agreement") dated as of August 15, 1993 with respect to warrants
(the "Seven-Year Warrants") to acquire common stock, par value $1.00 per share
of the Bank (the "Bank Common Stock");

   WHEREAS, pursuant to the terms of that certain Agreement and Plan of
Reorganization (the "Reorganization Agreement") dated as of May 28, 1997 by and
among the Bank, Golden State and Glendale Interim Federal Savings Bank, among
other things, (i) Golden State will become the holding company for the Bank, and
(ii) the Seven-Year Warrants will become exercisable, in accordance with their
terms and without the necessity of any exchange by the holders thereof, solely
to receive the number of shares of common stock, par value $1.00 per share of
Golden State (the "Golden State Common Stock") that equals the number of shares
of Bank Common Stock for which the Seven-Year Warrants were exercisable
immediately prior to the effective time (the "Effective Time") of the
reorganization transaction provided for in the Reorganization Agreement (the
"Reorganization"); and

   WHEREAS, the parties hereto desire to amend the Warrant Agreement to reflect
the transactions comprising the Reorganization and their effects.

   NOW THEREFORE, the parties hereto hereby agree as follows:

   1.    The term "Bank Common Stock" as used in the Warrant Agreement shall
mean Golden State Common Stock instead of Bank Common Stock.

   2.    All references to the "Bank" or the "Company" in Articles III and IV of
the Warrant Agreement shall be deemed to refer to Golden State instead of the
Bank.

   3.    All references to the "Bank" in Sections 6.01 and 6.05 shall be deemed
to refer to both the Bank and Golden State.

   4.    As provided in the Reorganization Agreement and pursuant to Section
3.01(e) of the Warrant Agreement, the Warrant Holders shall have the right to
exercise their Warrants for the number of shares of Golden State Common Stock
that such Warrant Holder would have been entitled to receive at the Effective
Time if such Warrant Holder had exercised their Warrants immediately prior
thereto.

                                       1

<PAGE>
 
   5.     Golden State shall cause the Warrant Agent to deliver the notice
required by Section 3.01(e) regarding this Amendment No. 1 to each Warrant
Holder.

   6.     Section 6.08 shall be amended in its entirety as follows:

   "Section 6.08 Notices. Any communication, notice or demand to be given
                 -------
hereunder shall be duly given if in writing and delivered, or sent by first
class mail, certified or registered, postage prepaid and addressed as follows:

          (a) If to the Bank or Golden State:

              414 N. Central Avenue 
              Glendale, California 91203 
              Attn: Corporate Secretary

              If to the Warrant Agent:

          (b) ChaseMellon Shareholder Services, LLC 
              400 South Hope Street 
              4th Floor
              Los Angeles, California 90071 
              Attn: Office Manager

          (c) If to a Warrant Holder, at such person's last known address as
such address shall appear on the registration books maintained by the Warrant
Agent.

          Any party may change the address to which any communication, notice or
demand shall be given by giving notice of such change in conformity with the
provisions of this Section."

   7.    This Amendment No. 1 shall be deemed effective as of the Effective
Time.

   8.    Except as otherwise specifically provided herein, the Warrant Agreement
shall remain unchanged.

                                       2

<PAGE>
 
   IN WITNESS WHEREOF, this Amendment No. 1 has been duly executed by the
parties hereto as of the day and year first above written.

                                                GLENDALE FEDERAL BANK, 
                                                FEDERAL SAVINGS BANK
                                                
                                                By: /s/ John E. Haynes
                                                    ----------------------------
                                                Title: EVP/CFO
                                                       -------------------------

                                                CHASEMELLON SHAREHOLDER
                                                SERVICES, LLC

                                                By: /s/ Michael E. Dzieciolowski
                                                    ----------------------------
                                                        Michael E. Dzieciolowski

                                                Title: Assistant Vice President
                                                       -------------------------

                                                GOLDEN STATE BANCORP INC. 

                                                By: /s/ John E. Haynes
                                                    ----------------------------
                                                Title:  CFO
                                                       -------------------------

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