Fourth Amendment to
             Agreement and Certificate of Limited Partnership of
                Geodyne Energy Income Limited Partnership II-H


     This Fourth  Amendment to Agreement and Certificate of Limited  Partnership
of Geodyne Energy Income Limited Partnership II-H (the "Partnership") is entered
into  by  and  between  Geodyne  Resources,   Inc.  ("Resources"),   a  Delaware
corporation,   as  successor  General  Partner,   Geodyne   Depositary   Company
("Depositary"),  a  Delaware  corporation,  as  the  Limited  Partner,  and  all
Substituted Limited Partners admitted to the Partnership.

     WHEREAS,  on May 17, 1989,  Geodyne  Properties,  Inc.  ("Properties"),  as
General partner, and Depositary executed and entered into that certain Agreement
and Certificate of Limited Partnership of the Partnership (the "Agreement"); and

     WHEREAS,  on February 25, 1993,  Properties  executed and entered into that
First  Amendment  to the  Agreement  whereby  it  changed  (i)  the  name of the
Partnership from "PaineWebber/Geodyne Energy Income Limited Partnership II-H" to
"Geodyne  Energy  Income  Limited  Partnership  II-H",  (ii) the  address of the
Partnership's  principal  place of  business,  and  (iii)  the  address  for the
Partnership's agent for service of process; and

     WHEREAS,  on August 4, 1993,  Properties  executed  and  entered  into that
Second Amendment to the Agreement  whereby it amended certain  provisions to (i)
expedite  the  method  of  accepting  transfers  of Unit  Holders'  Units in the
Partnership  and (ii)  provide  for an optional  right of  repurchase/redemption
which may be exercised by the Unit Holders; and

     WHEREAS,  on August 31,  1995,  Properties  executed  and entered into that
Third Amendment to the Agreement whereby it amended certain  provisions to allow
transfers  of Units  facilitated  through a matching  service to the extent that
such  transfers   otherwise   comply  with  Internal  Revenue  Service  transfer
regulations  applicable  to  non-permitted  transfers  for  non-publicly  traded
limited partnerships; and

     WHEREAS, Section 11.1 of the Agreement provides that the general partner of
the partnership (the "General  Partner") may, without prior notice or consent of
any Unit  Holder (as  defined in the  Agreement),  amend any  provision  of this
Agreement if, in its opinion,  such amendment  does not have a material  adverse
effect upon the Unit Holders; and

     WHEREAS,   Properties  merged  with  and  into  Geodyne  Resources,  Inc.
("Resources"), its parent corporation, effective June 30, 1996; and



                                      -1-
<PAGE>




     WHEREAS, Section 6.2 of the Agreement provides that the General Partner may
assign its General  Partner  Interest to a Person which shall become a successor
General Partner without the Consent of the Depositary,  if such assignment is in
connection with a merger; and

     WHEREAS,  as a result of the merger of Properties  with and into Resources,
ownership  of the General  Partner  Interest in the  Partnership  is assigned to
Resources by operation of law; and

     WHEREAS,  as a result of the merger of Properties  with and into Resources,
Resources  has  now  succeeded  to  the  position  of  General  Partner  of  the
Partnership; and

     WHEREAS,  Resources, as General Partner,  desires to amend the Agreement in
order to reflect Resources as the new General Partner.

     NOW,  THEREFORE,   in  consideration  of  the  covenants,   conditions  and
agreements herein contained, the parties hereto hereby agree as follows:

       All references in the Agreement to Geodyne Properties,  Inc. as General
       Partner are hereby  amended to  reflect,  instead,  Geodyne  Resources,
       Inc. as General Partner.

       IN WITNESS  WHEREOF,  the parties hereto have hereunto set their hands as
of the 1st day of July, 1996.


                                       Geodyne Properties, Inc.
                                       by Geodyne Resources, Inc.
                                       as successor by merger

                                       By:  /s/ Dennis R. Neill
                                            ----------------------------
                                            Dennis R. Neill
                                            President


                                       Geodyne Resources, Inc.
                                       as General Partner

                                       By:  /s/ Dennis R. Neill
                                            ----------------------------
                                            Dennis R. Neill
                                            President

                                       Geodyne Depositary Company, as the
                                       Limited Partner

                                       By:  /s/ Dennis R. Neill
                                            ----------------------------
                                            Dennis R. Neill
                                            President



                                      -2-
<PAGE>




                                       Geodyne Resources, Inc., as
                                       Attorney-in-Fact for all Substituted
                                       Limited Partners

                                       By:  /s/ Dennis R. Neill
                                            ----------------------------
                                            Dennis R. Neill
                                            President


                                      -3-