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                                  Exhibit 4.4
                  
     
               SECOND AMENDMENT TO RIGHTS AGREEMENT

   THIS SECOND AMENDMENT, dated as of April 16 , 1997, is between BHC 
Financial, Inc., a Delaware corporation (the "Corporation"), and American
Stock Transfer and Trust Company (the "Rights Agent").

                             RECITALS

   A.     The Corporation and the Rights Agent are parties to a Rights 
Agreement, dated as of November 12, 1996, as amended by the First Amendment 
thereto dated as of March 2, 1997 (as so amended, the "Rights Agreement").

   B.     Pursuant to Section 27 of the Rights Agreement, the Corporation and 
the Rights Agent desire to amend the Rights Agreement as set forth below:

   Accordingly, the parties agree as follows:

   1.     AMENDMENT OF SECTION 7 (a).  Section 7(a) of the Rights Agreement
is amended to read in its entirety as follows:

   "Except as otherwise provided herein, the Rights shall become exercisable
on the Distribution Date, and thereafter the registered holder of any Right
Certificate may, subject to Section 11(a)(ii) hereof and except as otherwise
provided herein, exercise the Rights evidenced thereby in whole or in part
upon surrender of the Right Certificate, with the form of election to 
purchase on the reverse side thereof duly executed, to the Rights Agent at 
the office or agency of the Rights Agent designated for such purpose, 
together with payment of the aggregate Purchase Price with respect to the 
total number of one one-hundredths of a share of Preferred Stock (or
other securities, cash or other assets, as the case may be) as to which the
Rights are exercised, at any time which is both after the Distribution Date
and prior to the time (the "Expiration Date") that is the earliest of (i)
the Close of Business on November 12, 2006 (the "Final Expiration Date"),
(ii) the time at which the Rights are redeemed as provided in Section 23 
hereof (the "Redemption Date"), (iii) the time at which such Rights are 
exchanged as provided in Section 24 hereof, or (iv) upon the effectiveness of 
the merger of the Company and Fiserv Delaware Sub, Inc. pursuant to and in
accordance with the Merger Agreement, dated as of March 2, 1997, among the
Corporation, Fiserv, Inc. and Fiserv Delaware Sub, Inc., as the same may be
amended from time to time."

   2.     EFFECTIVENESS.  This Amendment shall be deemed effective as of the 
date set forth above.  Except as amended hereby, the Rights Agreement shall
remain in full force and effect and shall be otherwise unaffected thereby.

   3.      MISCELLANEOUS.  This Amendment shall be deemed to be a contract
made under the laws of the State of Delaware and for all purposes shall be
governed by and construed in accordance with the laws of such state 
applicable to contracts to be made and performed entirely within such state. 
This Amendment may be executed in any number of counterparts, each of
such counterparts shall for all purposes be deemed to be an original, and
all such counterparts shall together constitute but one and the same
instrument.  If any term, provision, covenant or restriction of this
Amendment is held by a court of competent jurisdiction or other authority to
be invalid, illegal, or unenforceable, the remainder of the terms,
provisions, covenants and restrictions of this Amendment shall remain in full 
force and effect and shall in no way be affected, impaired or invalidated.

    EXECUTED as of the date set forth above.


                                 BHC FINANCIAL, INC.



                                 By:  /s/ William T. Spane
                                     -------------------------------------
                                     President and Chief Executive Officer




                                    AMERICAN STOCK TRANSFER AND
                                     TRUST COMPANY



                                 By: /s/  Herbert J. Lemmer 
                                     -----------------------------------
                                     Vice President