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

      This Third 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  Properties,  Inc.  ("Properties"),  a  Delaware
corporation,  as 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,  Properties 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
certain  First  Amendment  to the  Agreement of Limited  Partnership  whereby it
changed (i) the name of the Partnership from "PaineWebber/Geodyne  Energy Income
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
certain Second Amendment to the Agreement in order 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,  Section 11.1 of the Agreement  provides that the General Partner
may, without prior notice or consent of any Unit Holder,  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 as General  Partner desires to amend the Agreement in
order to allow transfers of Units facilitated  through a matching service to the
extent they otherwise comply with Internal Revenue Service transfer  regulations
applicable  to   non-permitted   transfers  for   non-publicly   traded  limited
partnerships.

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

      I.    Section 8.1.A(ii) of the Agreement is hereby deleted.

      II.   The  remaining  subsections  of Section  8.1A shall be  renumbered
            accordingly.




                                      -1-
<PAGE>



      IN WITNESS WHEREOF, the parties hereto have hereunto set their hands as of
this 31st day August, 1995.

                                    GEODYNE PROPERTIES, INC.
                                    as General Partner

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

                                    GEODYNE DEPOSITARY COMPANY,
                                    as the Limited Partner

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


                                    GEODYNE PROPERTIES, INC.,
                                    as Attorney-in-Fact for all
                                    Substituted Limited Partners


                                    By:   /s/ Drew S. Phillips
                                          ------------------------------
                                          Drew S. Phillips
                                          Vice President-Controller


                                      -2-