<PAGE>
                                                                   EXHIBIT 10.4b

                              INSTRUMENT AMENDING

                        LYONDELL PETROCHEMICAL COMPANY

                            EXECUTIVE MEDICAL PLAN


LYONDELL PETROCHEMICAL COMPANY hereby amends the Lyondell Petrochemical Company

Executive Medical Plan, effective November 1, 1996, to read as follows:


Section 3, COVERAGE, Subsection 3.2, Percentages Payable, is amended to read as
follows:


     3.2. Percentages Payable.  The Plan shall pay Benefits, other than
          Prescription Drug Benefits, at 100% of Reasonable Charges, unless
          otherwise provided. The Plan shall pay Prescription Drug Benefits at
          100% of Reasonable Charges in excess of the copayment if the
          Reasonable Charge for the Prescription Drug is greater than the
          copayment.

          Benefits shall be paid after satisfaction of all terms, conditions and
          limitations of this Plan.  Only charges that, in the opinion of the
          Claims Administrator, are Reasonable Charges will be considered as
          Covered Medical Expenses for which reimbursement may be obtained.

          Coverage at 100%, or 100% less copayment for Prescription Drug
          Benefits, shall not apply to expenses for which Benefits are payable
          under any other "plan," as defined in the section entitled
          "Coordination of Benefits."  For such expenses, the Plan shall not pay
          more than a reduced amount which, when added to Benefits payable under
          the Coordination of Benefits section, will not exceed 100% of
          Reasonable Charges or 100% of Reasonable Charges less copayment for
          Prescription Drugs covered under this Plan.



Section 3, COVERAGE, is amended to add new Subsection 3.8, Special Prescription

Drug Program, to read as follows:
<PAGE>
 
     3.8  Special Prescription Drug Program.

          (A)  In General. Benefits will be paid for a Prescription Drug that is
               dispensed by a Pharmacy for treatment of a Sickness or Injury at
               100% of Reasonable Charges in excess of the copayment, if the
               Reasonable Charge for the Prescription Drug is greater than the
               amount of the copayment.

               Copayments for brand names and generic drugs are as follows:
                    Prescription Drug Copayments

                    Local Purchase
                           Generic                     $ 3.00
                           Brand Name                  $10.00


                    Mail Order (31-90 day supply)
                         Generic                       $ 5.00
                         Brand Name                    $15.00

               The copayment with respect to brand name drugs shall apply to any
               brand name drug that is dispensed unless there is no generic
               equivalent to the brand name drug or the Pharmacy is unable to
               provide the generic drug at the time the prescription is
               presented. If the Pharmacy participates in the Special
               Prescription Drug Program, the Covered Person need only pay the
               applicable copayment at the time he obtains his Prescription Drug
               in order to receive the Benefits under the Plan. If the Pharmacy
               does not participate in the Special Prescription Drug Program,
               the Covered Person must pay the entire cost of the Prescription
               Drug at the time the Prescription Drug is obtained and must
               submit a claim in order to receive Benefits under the Plan.
               Notwithstanding any other provision of this Plan to the contrary,
               Benefits will be paid under this Special Prescription Drug
               Program for Prescription Drugs that (i) are Covered Mental Health
               Problem Expenses and (ii) comply with all other requirements of
               the Special Prescription Drug Program.

          (B)  Mail Order. A Covered Person may, at his option, elect to obtain
               his Prescription Drugs from a Mail Order Pharmacy and will
               receive Benefits at 100% of the Reasonable Charge in excess of
               the Copayment for mail order drugs. With respect to the Mail
               Order Pharmacy, the Covered Person need only pay the applicable
               copayment at the time he obtains his Prescription Drug in order
               to receive the Benefits under the Plan.

                                       2
<PAGE>
 
          (C)  Limitation on Special Prescription Drug Benefits. Notwithstanding
               any other provision of this Plan to the contrary, Benefits will
               not be payable under the terms of this Special Prescription Drug
               Program for the following charges:

               (1)  For items that are not Prescription Drugs and that are not
                    ordered by a Physician;

               (2)  For any drug that is entirely consumed at the time and place
                    it as prescribed;

               (3)  For less than a 30-day or more than a 90-day supply of a
                    Prescription Drug that is dispensed on a single occasion by
                    a Mail Order Pharmacy;

               (4)  For any injectable agent except insulin;

               (5)  For the administration or injection of any drug;

               (6)  For any contraceptive drug except oral contraceptives;

               (7)  For more than a 30-day supply per prescription or refill
                    from a Pharmacy other than a Mail Order Pharmacy;

               (8)  For any refill of a drug if it is more than the number of
                    refills specified by the Prescribing Physician; if the
                    prescriber has not specified the number of refills, or if
                    the frequency or number of prescriptions or refills appears
                    excessive under accepted medical practice standards, the
                    Claims Administrator, before recognizing charges, may
                    require a new Prescription or evidence as to need.

               (9)  For any refill of a Prescription Drug dispensed more than
                    one year after the latest Prescription for it or as
                    permitted by law of the jurisdiction in which the
                    Prescription Drug is dispensed;

               (10) For any Prescription Drug provided by or while the person is
                    an inpatient in any health care facility;

               (11) For any Prescription Drug provided on an outpatient basis in
                    any such institution to the extent Benefits are paid for it
                    under any other part of this Plan or any other program
                    sponsored by the Company;

               (12) For any Prescription Drug for which Benefits are actually
                    paid under any other part of this Plan.

                                       3
<PAGE>
 
and Sections 3.8 and 3.9 are renumbered as Sections 3.9 and 3.10, respectively.


Section 6, CONTINUATION COVERAGE (COBRA), Subsection 6.1,  Entitlement to COBRA
Coverage, 

Subpart (C), is amended to read as follows:

          (C)  Covered as a Dependent. If a Covered Person is covered by the
               Plan as a Dependent Child of an Executive, he has the right to
               elect COBRA coverage for himself if he loses coverage for any of
               the reasons in (A) or (B) above, or if he ceases to be a
               Dependent Child eligible for Coverage under the Plan.

               For purposes of eligibility for COBRA coverage, a Dependent Child
               shall include a Child born to or placed for adoption with a
               Covered Person who was an Executive during the period of COBRA
               Coverage applicable to that Covered Person. Coverage shall begin
               as of the same date for applicable Coverage for Dependents under
               Section 2.4.


Section 6, CONTINUATION COVERAGE (COBRA), Subsection 6.3, Notice of COBRA

Events, paragraph 2, is amended to read as follows:

          If a Covered Person elects COBRA coverage due to an employment
          termination (other than gross misconduct) or reduction in hours and
          the Social Security Administration determines that the Covered Person
          was disabled within the first 60 days of COBRA coverage, he must
          notify the Claims Administrator within the 18-month period described
          below. He also must notify the Claims Administrator within 30 days
          after the date he is determined to be no longer disabled.



Section 6, CONTINUATION COVERAGE (COBRA), Subsection 6.4, Duration of COBRA

Coverage, is amended to read as follows:


          6.4. Duration of COBRA Coverage. If a Covered Person does not elect
               COBRA coverage when it is offered to him, his coverage under the
               Plan will end. If he elects COBRA coverage, his coverage will be
               identical to the coverage provided under the Plan to similarly
               situated Executives or Dependents, as of the time

                                       4
<PAGE>
 
          coverage is being provided. This means that if the coverage for
          similarly situated Executives or Dependents is modified, his coverage
          will be modified in the same manner. COBRA coverage generally will
          last for 36 months unless the Covered Person lost coverage because of
                             ------
          a termination of employment (other than gross misconduct) or reduction
          in hours of employment, in which case, COBRA coverage will last for
          only 18 months. The 18-month coverage period may be extended to 29
          months if the Covered Person is determined to be disabled by the
          Social Security Administration within the first 60 days of COBRA
          coverage, provided that the Covered Person notifies the Company before
          the end of the 18-month period.

          If the Covered Person who is an Executive becomes entitled to
          Medicare, the maximum duration of COBRA coverage for qualified
          beneficiaries, other than the Covered Person who is an Executive,
          whether coverage is acquired as a result of eligibility for Medicare
          or other subsequent event, is 36 months from the date of the
          determination of Medicare eligibility.

          Special rules govern the COBRA coverage period when a Retiree or his
          family member loses coverage because of the commencement of bankruptcy
          proceedings concerning the Company, or if certain qualifying events
          occur within 18 or 29 months of a termination or reduction in hours of
          employment.



IN WITNESS WHEREOF, LYONDELL PETROCHEMICAL COMPANY, acting by and through its
duly authorized officer, has caused this Instrument to be executed on this 19th
day of December, 1996.



ATTEST:                             LYONDELL PETROCHEMICAL COMPANY



By:/s/ G.A. O'Brien                  By:/s/ Richard W. Park         
   --------------------------           ---------------------------
     Assistant Secretary                  Richard W. Park
                                          Vice President, Human Resources

                                       5