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


     This Second  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
First  Amendment  to the  Agreement  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,  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 (i) reflect the name change and address changes  described above,  (ii)
expedite  the  method  of  accepting  transfers  of Unit  Holders'  Units in the
Partnership  and (iii)  provide for an optional  right of  repurchase/redemption
which may be exercised by the Unit Holders.

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

I.     The third sentence  contained in Section 7.3 of the Agreement is hereby
       amended and restated as follows:

            Unit Holders becoming  Substituted Limited Partners will be admitted
            to the Partnership monthly.




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II.    The second  sentence  contained  in Section 7.3 of the  Agreement,  which
       sentence  required  the  payment by Unit  Holders of a fee (not to exceed
       $100) for legal and administrative  costs associated with the transfer of
       a Partnership Unit, is hereby deleted.

III.   Section 8.2B(3) of the Agreement,  which section  required the payment by
       Unit  Holders of a fee (not to exceed $50) for expenses  associated  with
       the General  Partner's  acceptance  of a Substituted  Limited  Partner is
       hereby deleted.

IV.    The  reference in the last sentence of Section 8.3A of the Agreement to
       a transfer fee is hereby deleted.

V.     The Agreement is hereby  amended to provide for a new Article  Fifteen.
       Said Article Fifteen is hereby stated as follows:


                                 Article Fifteen

                   Optional Repurchase/Redemption Provisions

            Section 15.1.  Optional Repurchase Right.

            Any Unit Holder or Substituted Limited Partner shall have the right,
      at his  option,  to  present  his  Units  to the  General  Partner  or its
      designated Affiliate for repurchase on the basis set forth in this Article
      Fifteen.

            Section 15.2.  Procedure for Repurchase.

            A. As of December 31, 1992 and annually  thereafter  (the "Appraisal
      Date") the General  Partner shall  appraise the Proved  Reserves and other
      assets of the Partnership  pursuant to the provisions set forth herein and
      shall  assign a  repurchase  price  (the  "Repurchase  Price") to the Unit
      Holders' Units in the  Partnership  in accordance  with the provisions set
      forth herein.

            B. In  arriving  at the  Repurchase  Price,  the  General  Partner
      shall consider those factors  deemed  relevant by it including,  without
      limitation, the following:

            (i)        the present  value of the  estimated  future
                       net     revenues    of    the     Production
                       Partnership's  Proved  Reserves,  calculated
                       as described below; and

            (ii)       the  book  value  of all  other  Partnership
                       assets and liabilities.





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             Section  15.3.  Calculation  of  Present  Value of the
      Partnership's Estimated Future Net Revenues.

            In  calculating  the present  value of the  Partnership's  Estimated
      Future  Net  Revenues  the  General   Partner   shall  use  the  petroleum
      engineering reports and other petroleum reserve information required to be
      furnished to the Unit Holders pursuant to Section 10.4C of the Agreement.

            Future gross revenues expected to be derived from the production and
      sale of the Proved Reserves  attributable to the Production  Partnership's
      Producing  Properties  shall be estimated  using either (i) escalations of
      future sales prices of  Hydrocarbons  supplied by the General Partner (the
      "Escalated  Case")  or (ii)  sales  prices  of  Hydrocarbons  provided  by
      Regulation S-X adopted by the Securities and Exchange Commission (the "SEC
      Case"), as the General Partner may determine in its sole discretion.

            Future net revenues  shall be  calculated  by deducting  anticipated
      expenses  (using either (i)  escalations  of future costs  supplied by the
      General  Partner if the General  Partner  adopted the Escalated  Case with
      respect to future sales prices of  Hydrocarbons  or (ii)  constant  future
      costs if the General  Partner  adopted the SEC Case with respect to future
      sales prices of Hydrocarbons) from estimated future gross revenues.

            The present value of the future net revenues  shall be calculated by
      discounting  the  estimated  future  net  revenues  at either  10% (if the
      General Partner  employed  future pricing  criteria in accordance with the
      SEC Case) or that rate per annum which is one percentage point higher than
      the prime  rate of  interest  of The Chase  Manhattan  Bank,  N.A.  or any
      successor bank, as of the Appraisal Date (if the General Partner  employed
      pricing criteria in accordance with the Escalated Case, provided, however,
      that such  discount rate will not exceed 18% per annum and will be no less
      than 10% per annum).

            Section 15.4.  Risk Reduction.

            In  determining  the Repurchase  Price for Unit Holders  pursuant to
      this  Article  Fifteen,  the  present  value of the  Partnership's  Proved
      Developed  Producing  Reserves  shall be  reduced  by 25% for risk and the
      present value of all other  categories of Proved Reserves shall be reduced
      by 35% for  risk.  The risk  reductions  shall be  subject  to  upward  or
      downward  adjustment by the General  Partner if, during the period between
      the Appraisal  Date and the Effective  Date (as defined in Section  15.5),
      there has been a material increase or decrease in the current price of oil
      or gas or in the estimated amount of the Partnership's Proved Reserves.



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            Section 15.5.  Tender Procedure.

            Upon completion of the appraisal of the  Partnership's  assets as of
      the Appraisal  Date, the General  Partner shall notify each Unit Holder of
      the Repurchase  Price and his  proportionate  share thereof and either the
      General  Partner or one of its Affiliates will offer to purchase such Unit
      Holder's Units in exchange for such Unit Holder's  proportionate  share of
      the Repurchase Price (a "Repurchase  Offer").  Any Unit Holder desiring to
      do so may accept such Repurchase Offer by notifying the General Partner of
      his  election.  Unit Holders so  notifying  the General  Partner  shall be
      referred to herein as "Electing Unit Holders".  The General Partner or its
      designated  Affiliate shall  thereupon  promptly pay to each Electing Unit
      Holder, his proper share of the Repurchase Price, calculated as herein set
      forth,  within 30 days from the date which a properly drawn  assignment of
      such  Electing  Unit  Holder's  interest,  free and clear of all liens and
      encumbrances,  is tendered to and  accepted by the General  Partner or its
      designated  Affiliate (the "Effective  Date").  Upon the acquisition of an
      Electing  Unit  Holder's  Units,  the  General  Partner or its  designated
      Affiliate shall, as of the Effective Date of such acquisition,  succeed to
      all the rights and obligations attributable to such interest.

            Section   15.6.   Monthly   Adjustment   to  Repurchase
            Price.

            The  Repurchase  Price  shall  be  recalculated   monthly  with  the
      Repurchase Price being reduced by the amount of any cash  distributions to
      Unit Holders  during the period from the Appraisal Date to the date of the
      payment of the Repurchase Price and shall otherwise be adjusted to reflect
      the effect of material  operations  during such  period.  In the event the
      Repurchase  Price is  adjusted  for any reason  other than to reflect  the
      payment of cash  distributions,  the General Partner shall provide written
      notification of such adjustment to the Unit Holders.

            Section 15.7.  Limitation on Units Repurchased.

            A. At the  sole  discretion  of the  General  Partner,  the  General
      Partner or its  designated  Affiliate may either (i) limit the time period
      in which it will accept  tendered  Units for  repurchase or (ii) limit the
      amount of Units to be accepted for repurchase;  provided, however, that in
      any event the annual  repurchase  offer will (i) remain  open for at least
      thirty (30) days and (ii) the General Partner or its designated  Affiliate
      will  offer to  repurchase  at least 10% of the  outstanding  Units of the
      Partnership. In such an event, the General Partner will either (i) specify
      such  limitation(s)  in the  annual  Repurchase  Offer  mailed to the Unit
      Holders or (ii) provide all Unit Holders with written notification of such
      limitation(s) at least thirty (30) days prior to the effective date of any
      such limitation(s).



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             B. In the event the General  Partner  imposes a limitation upon the
      number of Units to be  repurchased in the  Partnership,  and the amount of
      Units  tendered,  but  not  repurchased,  exceeds  such  limitation,  such
      tendered Units will be accepted for repurchase by lot.

            C. In  addition,  in order to avoid  certain  possible  adverse  tax
      consequences,  the  General  Partner  may,  in  order to  comply  with the
      regulations  or procedures  under Section  469(k) of the Internal  Revenue
      Code of 1986, as amended,  relating to "publicly traded partnerships," (i)
      delay or defer the  Effective  Date of any  repurchase  and (ii) limit the
      total number of Units of any Partnership to be repurchased in any 12-month
      period to the maximum number provided in such  regulations and procedures.
      In the event of such delay or deferral,  the General  Partner shall notify
      the Electing  Unit Holder of the reasons  therefor  and shall  provide the
      Electing  Unit Holder with the option to withdraw  his tender of Units for
      repurchase.

       IN WITNESS  WHEREOF,  the parties hereto have hereunto set their hands as
of the 4th day of August, 1993.

                                       Geodyne Properties, Inc.
                                       as General Partner

                                       By:  /s/ C. Philip Tholen
                                            ----------------------------
                                            C. Philip Tholen
                                            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


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