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                                                                   EXHIBIT 10.31

                                  ATTACHMENT B

      As a supplement to the letter agreement dated October 7, 2004 between La
Jolla Pharmaceutical Company ("LJP") and Josefina Elchico. ("ELCHICO") related
to Elchico's employment by LJP, Elchico and LJP hereby agree as follows:

      In connection with Elchico's employment with LJP, LJP's management will
recommend to LJP's Board of Directors that LJP grant to Elchico an option to
purchase up to 50,000 shares of common stock of LJP. Such option, if granted,
shall be the "OPTION" for purposes hereof.

      If Elchico's employment is terminated by LJP without cause (as defined
below), or if a Change in Control of LJP (as defined below) occurs and Elchico's
employment with LJP or its successor "terminates in connection with" (as defined
below) that Change in Control and in the absence of any event or circumstance
constituting Cause, then:

      (i)   Elchico will be entitled to receive from LJP a severance payment
            equal to her then-current base salary for a period of six full
            calendar months from the date of termination and an additional three
            full calendar months if and when after the first six months he has
            not found suitable employment, payable consistent with LJP's normal
            payroll practices, provided that such payment will be contingent
            upon execution and delivery by Elchico and LJP of a mutual release,
            in form satisfactory to LJP, of all claims arising in connection
            with Elchico's employment with LJP and termination thereof, and

      (ii)  Elchico will be entitled to receive for a period of six full
            calendar months from the date of termination and an additional three
            full calendar months if and when after the first six months she has
            not found suitable employment, medical and dental benefits coverage
            for Elchico and/or her dependents through the Company's available
            plans at the time and LJP will be responsible to continue payment of
            all applicable deductions for premium costs. After Company's
            obligation to pay the premiums for health and dental coverage
            Elchico and/or her dependents will be eligible to continue plan
            participation under COBRA.

      (iii) Notwithstanding anything to the contrary in the option plan (the
            "PLAN") pursuant to which all of Elchico's existing options were
            granted, the Options shall automatically vest and become fully
            exercisable as of the date of termination of Executive's employment
            (the "TERMINATION DATE"), notwithstanding any vesting or performance
            conditions applicable thereto, and shall remain exercisable for a
            period of one year following the Termination Date or such longer
            period as is provided by the Plan or grant pursuant to which the
            Options were granted. However, notwithstanding the foregoing, in no
            case will the Options be exercisable beyond the duration of the
            original term thereof, and if the Options qualify as an incentive
            stock option under the Internal Revenue Code and applicable
            regulations thereunder, the exercise period thereof shall not be
            extended in such a manner as to cause the Options to cease to
            qualify as an incentive stock option unless Executive elects to
            forego incentive stock option treatment and extend the exercise
            period thereof as provided herein.

For purposes hereof, "CHANGE IN CONTROL" of LJP has the meaning set forth in the
Plan in its form as the date of grant of the Options.

For purposes hereof, "CAUSE" means Elchico has (i) engaged in serious criminal
activity or other wrongful conduct that has an adverse impact on LJP, (ii)
disregarded instructions given to him under the authority of LJP's Board of
Directors, (iii) performed services for any person or entity other than LJP and
appropriate civic organizations, or (iv) otherwise materially breached her
employment or fiduciary responsibilities to LJP.

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For purposes hereof, Elchico's employment with LJP or its successor will be
deemed to "TERMINATE IN CONNECTION WITH" a Change in Control if, within 180 days
after the consummation of the Change of Control, (i) Elchico is removed from
Elchico's employment by, or resigns her employment upon the request of, a person
exercising practical voting control over LJP or its successor following the
Change in Control or a person acting upon authority or at the instruction of
such person; or (ii) Elchico's position is eliminated as a result of a reduction
in force made to reduce over-capacity or unnecessary duplication of personnel
and Elchico is not offered a replacement position with LJP or its successor as a
Vice President with compensation and functional duties substantially similar to
the compensation and duties in effect immediately before the Change in Control;
or (iii) Elchico resigns her employment with the Company or its successor rather
than comply with a relocation of her primary work site more than 50 miles from
LJP's headquarters.

      In Witness Whereof, LJP and Elchico have entered into this agreement as of
October 12, 2004.

La Jolla Pharmaceutical Company

By: /s/ Steven B. Engle                        /s/ Josefina Elchico
    -------------------                        --------------------
    Steven B. Engle                            Josefina Elchico
    Chairman & CEO                             Vice President, Quality Systems

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