<PAGE>
                                                                   EXHIBIT 10.4


                      NON-QUALIFIED STOCK OPTION AGREEMENT
                                   under the
               ACCREDO HEALTH, INCORPORATED AND ITS SUBSIDIARIES
                STOCK OPTION AND RESTRICTED STOCK PURCHASE PLAN


                  Optionee:         Kenneth J. Melkus
                           ----------------------------------------------------

                  Number Shares Subject to Option:            20,000
                                                  -----------------------------

                  Exercise Price per Share:          $35.36
                                           ------------------------------------

                  Date of Grant:                     November 1, 2001
                                -----------------------------------------------


         1.       Grant of Option. Accredo Health, Incorporated (the "Company")
hereby grants to the Optionee named above (the "Optionee"), under the Accredo
Health, Incorporated and its Subsidiaries Stock Option and Restricted Stock
Purchase Plan (the "Plan"), a Non-Qualified Stock Option to purchase, on the
terms and conditions set forth in this agreement (this "Option Agreement"), the
number of shares indicated above of the Company's $0.01 par value common stock
(the "Stock"), at the exercise price per share set forth above (the "Option").
Capitalized terms used herein and not otherwise defined shall have the meanings
assigned such terms in the Plan.

         2.       Vesting of Option. The Option shall be 100% vested upon the
date of grant.

         3.       Period of Option and Limitations on Right to Exercise. The
Option will, to the extent not previously exercised, lapse under the earliest
of the following circumstances; provided, however, that the Committee may,
prior to the lapse of the Option under the circumstances described in paragraph
below, provide in writing that the Option will extend until a later date:

         (a)      The Option shall lapse as of 5:00 p.m., Eastern Time, on the
tenth anniversary of the date of grant (the "Expiration Date").

         (b)      The Option shall lapse three months after the Optionee's
termination of service as a director for any reason.

         4.       Exercise of Option. The Option shall be exercised by written
notice directed to the Secretary of the Company at the principal executive
offices of the Company, in substantially the form attached hereto as Exhibit A,
or such other form as the Committee may approve. Unless the exercise is a
broker-assisted "cashless exercise" as described below, such written notice
shall be accompanied by full payment in cash,


<PAGE>


shares of Stock previously acquired by the Optionee, or any combination
thereof, for the number of shares specified in such written notice; provided,
however, that if shares of Stock are used to pay the exercise price, such
shares must have been held by the Optionee for at least six months. The Fair
Market Value of the surrendered Stock as of the last trading day immediately
prior to the exercise date shall be used in valuing Stock used in payment of
the exercise price. To the extent permitted under Regulation T of the Federal
Reserve Board, and subject to applicable securities laws, the Option may be
exercised through a broker in a so-called "cashless exercise" whereby the
broker sells the Option shares and delivers cash sales proceeds to the Company
in payment of the exercise price. In such case, the date of exercise shall be
deemed to be the date on which notice of exercise is received by the Company
and the exercise price shall be delivered to the Company on the settlement
date.

         Subject to the terms of this Option Agreement, the Option may be
exercised at any time and without regard to any other option held by the
Optionee to purchase stock of the Company. Upon the Optionee's death, the
Option may be exercised by the Optionee's beneficiary.

         5.       Beneficiary Designation. The Optionee, by written notice to
the Committee, may designate one or more persons (and from time to time change
such designation) including the Optionee's legal representative, who, by reason
of the Optionee's death, shall acquire the right to exercise all or a portion
of the Option. If no beneficiary has been designated or survives the Optionee,
the Option may be exercised by the personal representative of the Optionee's
estate. If the person with exercise rights desires to exercise any portion of
the Option, such person must do so in accordance with the terms and conditions
of this Agreement and the Plan.

         6.       Withholding. The Company has the authority and the right to
deduct or withhold, or require the Optionee to remit to the Company, an amount
sufficient to satisfy federal, state, and local taxes (including the Optionee's
FICA obligation) required by law to be withheld with respect to any taxable
event arising as a result of the exercise of the Option. Such withholding
requirement may be satisfied, in whole or in part, at the election of the
Company, by withholding from the Option shares of Stock having a Fair Market
Value on the date of withholding equal to the minimum amount (and not any
greater amount) required to be withheld for tax purposes, all in accordance
with such procedures as the Committee establishes.

         7.       Limitation of Rights. The Option does not confer to the
Optionee or the Optionee's personal representative any rights of a shareholder
of the Company unless and until shares of Stock are in fact issued to such
person in connection with the exercise of the Option. Nothing in this Option
Agreement shall confer upon the Optionee any right to continue as a director of
the Company or any Parent or Subsidiary.

         8.       Stock Reserve. The Company shall at all times during the term
of this Option Agreement reserve and keep available such number of shares of
Stock as will be sufficient to satisfy the requirements of this Option
Agreement.


                                      -2-
<PAGE>


         9.       Restrictions on Transfer and Pledge. The Option may not be
pledged, encumbered, or hypothecated to or in favor of any party other than the
Company or a Parent or Subsidiary, or be subject to any lien, obligation, or
liability of the Optionee to any other party other than the Company or a Parent
or Subsidiary. The Option is not assignable or transferable by the Optionee
other than by will or the laws of descent and distribution or pursuant to a
domestic relations order that would satisfy Section 414(p)(1)(A) of the Code;
provided, however, that the Committee may (but need not) permit other transfers
where the Committee concludes that such transferability (i) does not result in
accelerated taxation and (ii) is otherwise appropriate and desirable, taking
into account any factors deemed relevant, including without limitation, state
or federal tax or securities laws applicable to transferable options. The
Option may be exercised during the lifetime of the Optionee only by the
Optionee or any permitted transferee.

         10.      Restrictions on Issuance of Shares. If at any time the Board
shall determine in its discretion, that listing, registration or qualification
of the shares of Stock covered by the Option upon any securities exchange or
under any state or federal law, or the consent or approval of any governmental
regulatory body, is necessary or desirable as a condition to the exercise of
the Option, the Option may not be exercised in whole or in part unless and
until such listing, registration, qualification, consent or approval shall have
been effected or obtained free of any conditions not acceptable to the Board.

         11.      Plan Controls. The terms contained in the Plan are
incorporated into and made a part of this Option Agreement and this Option
Agreement shall be governed by and construed in accordance with the Plan. In
the event of any actual or alleged conflict between the provisions of the Plan
and the provisions of this Option Agreement, the provisions of the Plan shall
be controlling and determinative.

         12.      Successors. This Option Agreement shall be binding upon any
successor of the Company, in accordance with the terms of this Option Agreement
and the Plan.

         13.      Severability. If any one or more of the provisions contained
in this Option Agreement are invalid, illegal or unenforceable, the other
provisions of this Option Agreement will be construed and enforced as if the
invalid, illegal or unenforceable provision had never been included.

         14.      Notice. Notices and communications under this Option
Agreement must be in writing and either personally delivered or sent by
registered or certified United States mail, return receipt requested, postage
prepaid. Notices to the Company must be addressed to:

                  Accredo Health, Incorporated
                  1640 Century Center Parkway
                  Suite 101
                  Memphis, Tennessee  38134
                  Attn:  Secretary



                                      -3-
<PAGE>


or any other address designated by the Company in a written notice to the
Optionee. Notices to the Optionee will be directed to the address of the
Optionee then currently on file with the Company, or at any other address given
by the Optionee in a written notice to the Company.

         15.      Binding Effect. The grant of the Options referenced herein is
subject to Optionee being bound by all of the terms set out in this Agreement.
The acceptance of the Options and the exercise of any right hereunder,
including but not being limited to the giving of written notice to exercise any
Option, shall constitute conclusive evidence of acceptance by the Optionee of
all of the terms, and conditions set out herein, and Optionee by such actions
shall be bound by, and shall be deemed to have agreed to these terms and
conditions, the same as if Optionee had affixed his or her signature to this
Stock Option Agreement.

         IN WITNESS WHEREOF, Accredo Health, Incorporated, acting by and
through its duly authorized officers, has caused this Option Agreement to be
executed, all as of the day and year first above written.


                                    ACCREDO HEALTH, INCORPORATED

                                    By: /s/   Thomas W. Bell, Jr.
                                       ----------------------------------------

                                    Name:    Thomas W. Bell, Jr.
                                         --------------------------------------

                                    Title:   Sr. VP and Secretary
                                          -------------------------------------


                                      -4-
<PAGE>


                                   EXHIBIT A

                    NOTICE OF EXERCISE OF OPTION TO PURCHASE
                                COMMON STOCK OF
                          ACCREDO HEALTH, INCORPORATED

Name
    -------------------------------------
Address:
        ---------------------------------
Date
    -------------------------------------


Accredo Health, Incorporated
1640 Century Center Parkway
Suite 101
Memphis, Tennessee  38134
Attn: Secretary

Re:      Exercise of Non-Qualified Stock Option

         I elect to purchase ______________ shares of Common Stock of Accredo
Health, Incorporated (the "Company") pursuant to the Accredo Health,
Incorporated Non-Qualified Stock Option Agreement dated ______________ and the
Accredo Health, Incorporated and its Subsidiaries Stock Option and Restricted
Stock Purchase Plan. The purchase will take place on the Exercise Date, which
will be (i) as soon as practicable following the date this notice and all other
necessary forms and payments are received by the Company, or (ii) in the case
of a Broker-assisted cashless exercise (as indicated below), the date of this
notice.

         On or before the Exercise Date (or, in the case of a Broker-assisted
cashless exercise, on the settlement date following the Exercise Date), I will
pay the full exercise price in the form specified below (check one):

[ ]      Cash Only: by delivering a check to the Company for $___________.

[ ]      Cash and Shares: by delivering a check to the Company for $_________
         for the part of the exercise price. I will pay the balance of the
         exercise price by delivering to the Company a stock certificate with
         my endorsement for shares of Company Stock that I have owned for at
         least six months. If the number of shares of Company Stock represented
         by such stock certificate exceeds the number needed to pay the
         exercise price, the Company will issue me a new stock certificate for
         the excess.

[ ]      Shares Only: by delivering to the Company a stock certificate with
         my endorsement for shares of Company Stock that I have owned for at
         least six


<PAGE>


         months. If the number of shares of Company Stock represented by such
         stock certificate exceeds the number needed to pay the exercise price,
         the Company will issue me a new stock certificate for the excess.

[ ]      Cash From Broker: by delivering the purchase price from
         _______________________, a broker, dealer or other "creditor" as
         defined by Regulation T issued by the Board of Governors of the
         Federal Reserve System (the "Broker"). I authorize the Company to
         issue a stock certificate in the number of shares indicated above in
         the name of the Broker in accordance with instructions received by the
         Company from the Broker and to deliver such stock certificate directly
         to the Broker (or to any other party specified in the instructions
         from the Broker) upon receiving the exercise price from the Broker.

         On or before the Exercise Date, I will satisfy any applicable tax
withholding obligations in the form specified below (check one):

[ ]      Cash Only: by delivering a check to the Company for the full tax
         withholding amount.

[ ]      Cash and Shares: by delivering a check to the Company for $_________
         for part of the tax withholding amount. I will pay the balance of the
         tax withholding amount by delivering to the Company a stock
         certificate with my endorsement for shares of Company Stock that I
         have owned for at least six months. If the number of shares of Company
         Stock represented by such stock certificate exceeds the number needed
         to pay the tax withholding amount, the Company will issue me a new
         stock certificate for the excess.

[ ]      Shares Only: by delivering to the Company a stock certificate with
         my endorsement for shares of Company Stock that I have owned for at
         least six months. If the number of shares of Company Stock represented
         by such stock certificate exceeds the number needed to pay the tax
         withholding amount, the Company will issue me a new stock certificate
         for the excess.

[ ]      Withholding of Shares to Cover Minimum Obligation: by having the
         Company withhold shares of Stock from the Option having a Fair Market
         Value on the date of withholding equal to the minimum amount (and not
         any greater amount) required to be withheld for tax purposes. Only
         whole shares may be withheld.


                                      -2-
<PAGE>


         Please deliver the stock certificate to me (unless I have chosen to
pay the purchase price through a Broker).


                                             Very truly yours,


                                             ----------------------------------

AGREED TO AND ACCEPTED:

ACCREDO HEALTH, INCORPORATED

By:
   ------------------------------------

Title:
      ---------------------------------

Number of Option Shares
Exercised:
          -----------------------------

Number of Option Shares
Remaining:
          -----------------------------

Date:
     ----------------------------------


                                      -3-