Exhibit 10.5.4

STOCK OPTIONS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

ADJUSTMENTS TO CARDINAL HEALTH STOCK OPTIONS AND TERMS OF CAREFUSION STOCK OPTIONS

August 31, 2009

As a result of the separation of the clinical and medical products businesses of Cardinal Health, Inc. (“Cardinal Health”) by means of a spin-off of those businesses to Cardinal Health’s shareholders, effective August 31, 2009 (the “Spin-Off”), outstanding stock option awards granted by Cardinal Health to you (the “Cardinal Health Options”) pursuant to the terms of equity incentive plans adopted by Cardinal Health (“Cardinal Health Equity Plans”) and related grant agreements (the “Cardinal Option Agreements”) are being adjusted, as of the effective time of the Spin-Off, as follows:

Adjusted Pre-2007 Cardinal Options and Adjusted Post-2007 Cardinal Options

Except for the adjusted exercise price and number of shares subject to each Pre-2007 Cardinal Option and Post-2007 Cardinal Option, your Adjusted Pre-2007 Cardinal Options and Adjusted Post-2007 Cardinal Options will continue to be governed by (i) your Cardinal Option Agreements, as amended (including the provisions in the agreements relating to “Triggering Conduct/Competitor Triggering Conduct” and “Special Forfeiture/Repayment Rules”) and (ii) the Cardinal Health Equity Plan under which the agreement was issued, also as amended. Therefore, among other terms, the extent to which each Adjusted Pre-2007 Cardinal Option and Adjusted Post-2007 Cardinal Option will vest and become exercisable on and after specific dates and the date on which such options will expire will be the same as those set forth in your Cardinal Option Agreements.

STOCK OPTIONS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

The adjusted exercise price and number of shares subject to each Adjusted Pre-2007 Cardinal Option and Adjusted Post-2007 Cardinal Option can be found on the website of Cardinal Health’s third-party equity plan administrator.

Please note that CareFusion Corporation (“CareFusion”) and its affiliates are third party beneficiaries of all rights that benefit CareFusion with respect to your Adjusted Pre-2007 Cardinal Options and Adjusted Post-2007 Cardinal Options and as a result CareFusion may enforce with full force and effect all terms and conditions that benefit CareFusion with respect to such options.

CareFusion Options

Your CareFusion Options are granted under, and subject to, the terms and conditions of the CareFusion Corporation 2009 Long-Term Incentive Plan. They are also subject to the terms of the Cardinal Option Agreement for the corresponding Cardinal Health Option (including provisions regarding “Triggering Conduct/Competitor Triggering Conduct” and “Special Forfeiture/Repayment Rules”) and the applicable Cardinal Health Equity Plan, which have been adjusted and restated on Appendix A attached hereto for purposes of applying them to your CareFusion Options and have been approved by the Human Resources and Compensation Committees of Cardinal Health and CareFusion. Please note that Cardinal Health and its affiliates are third party beneficiaries of all rights that benefit Cardinal Health with respect to your CareFusion Options and as a result Cardinal Health may enforce with full force and effect all terms and conditions that benefit Cardinal Health with respect to such options.

STOCK OPTIONS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

Appendix A

CAREFUSION CORPORATION

NONQUALIFIED STOCK OPTION TERMS AND CONDITIONS

These Nonqualified Stock Option Terms and Conditions (the “Terms”) adjust and restate the terms that apply to the Cardinal Health Options (as defined below) for purposes of applying such terms to the nonqualified stock options (the “CareFusion Options”) granted to Awardee by CareFusion Corporation (the “Company”) under the CareFusion Corporation 2009 Long-Term Incentive Plan (the “Plan”) as a result of the separation of the clinical and medical products businesses of Cardinal Health, Inc. (“Cardinal Health”) by means of a spin-off of at least 80.1% of the outstanding common stock of the Company to Cardinal Health’s shareholders, effective on August 31, 2009 (the “Spin-Off”). These Terms, together with the Option Terms (as defined below) and the Plan, shall govern the CareFusion Options. The CareFusion Options are Replacement Awards under the Plan.

The “Number of Shares” that are covered by the CareFusion Options and the “Exercise Price per Share” of the CareFusion Options constitute the option terms (the “Option Terms”) and can be found on the website of the Company’s third-party equity plan administrator. The extent to which the CareFusion Options shall vest and become exercisable on and after specific dates (the “Vesting Date(s)”), subject in each case to the provisions of these Terms, including those relating to Awardee’s continued service with Cardinal Health and its Affiliates (collectively, the “Cardinal Group”) and the date on which the CareFusion Options shall expire (the “Grant Expiration Date”) are the same terms as those set forth in Awardee’s stock option agreement(s) (each, a “Cardinal Option Agreement”) for stock option awards granted to Awardee by Cardinal Health (the “Cardinal Health Options”) on the grant date specified in the agreement for such Cardinal Health Options (the “Pre-Spin Grant Date”).

Capitalized terms used in these Terms which are not specifically defined herein will have the meanings ascribed to such terms in the Plan.

1. Method of Exercise and Payment of Price.

(a) Method of Exercise. At any time when all or a portion of the CareFusion Options is exercisable under the Plan and these Terms, some or all of the exercisable portion of the CareFusion Options may be exercised from time to time by written notice to the Company, or such other method of exercise as may be specified by the Company, including, without limitation, exercise by electronic means on the website of the Company’s third-party equity plan administrator, which will:

(i) state the number of whole Shares with respect to which the CareFusion Options are being exercised; and

(ii) if the CareFusion Options are being exercised by anyone other than Awardee, if not already provided, be accompanied by proof satisfactory to counsel for the Company of the right of such person or persons to exercise the CareFusion Options under the Plan and all Applicable Laws and regulations.

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STOCK OPTIONS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

(b) Payment of Price. The full exercise price for the portion of the CareFusion Options being exercised shall be paid to the Company as provided below:

(i) in cash;

(ii) by check or wire transfer (denominated in U.S. Dollars);

(iii) subject to any conditions or limitations established by the Administrator, other Shares which (A) in the case of Shares acquired from the Company (whether upon the exercise of the CareFusion Options or otherwise), have been owned by the Participant for more than six (6) months on the date of surrender (unless this condition is waived by the Administrator), and (B) have a Fair Market Value on the date of surrender equal to or greater than the aggregate exercise price of the Shares as to which said CareFusion Options shall be exercised (it being agreed that the excess of the Fair Market Value over the aggregate exercise price shall be refunded to Awardee, with any fractional Share being repaid in cash);

(iv) consideration received by the Company under a broker-assisted sale and remittance program acceptable to the Administrator; or

(v) any combination of the foregoing methods of payment.

2. Transferability. The CareFusion Options shall be transferable (I) at Awardee’s death, by Awardee by will or pursuant to the laws of descent and distribution, and (II) by Awardee during Awardee’s lifetime, without payment of consideration, to (a) the spouse, former spouse, parents, stepparents, grandparents, parents-in-law, siblings, siblings-in-law, children, stepchildren, children-in-law, grandchildren, nieces or nephews of Awardee, or any other persons sharing Awardee’s household (other than tenants or employees) (collectively, “Family Members”), (b) a trust or trusts for the primary benefit of Awardee or such Family Members, (c) a foundation in which Awardee or such Family Members control the management of assets, or (d) a partnership in which Awardee or such Family Members are the majority or controlling partners; provided, however, that subsequent transfers of the transferred CareFusion Options shall be prohibited, except (X) if the transferee is an individual, at the transferee’s death by the transferee by will or pursuant to the laws of descent and distribution, and (Y) without payment of consideration to the individuals or entities listed in subparagraphs II(a), (b) or (c), above, with respect to the original Awardee. The Administrator may, in its discretion, permit transfers to other persons and entities as permitted by the Plan. Neither a transfer under a domestic relations order in settlement of marital property rights nor a transfer to an entity in which more than 50% of the voting interests are owned by Awardee or Family Members in exchange for an interest in that entity shall be considered to be a transfer for consideration. Within ten (10) days of any transfer, Awardee shall notify the Compensation and Benefits department of the Company in writing of the transfer. Following transfer, the CareFusion Options shall continue to be subject to the same terms and conditions as were applicable immediately prior to transfer and, except as otherwise provided in the Plan or these Terms, references to the original Awardee shall be deemed to refer to the transferee. The effects of Awardee’s termination of service on the Cardinal Board (as defined below) provided in paragraph 3 hereof shall continue to be applied with respect to the original Awardee, following which the CareFusion Options shall be exercisable by the transferee only to the extent, and for the periods, specified in paragraph 3. The Company shall have no obligation to notify any transferee of Awardee’s termination of service on the Cardinal Board for any reason. The conduct prohibited of Awardee in paragraphs 5 and 6 hereof shall continue to be prohibited of Awardee following transfer to the same extent as

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STOCK OPTIONS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

immediately prior to transfer and the CareFusion Options (or its economic value, as applicable) shall be subject to forfeiture by the transferee and recoupment from Awardee to the same extent as would have been the case of Awardee had the CareFusion Options not been transferred. Awardee shall remain subject to the recoupment provisions of paragraphs 5 and 6 of these Terms following transfer of the CareFusion Options.

3. Termination of Service on the Board.

(a) Termination of Service by Death. If Awardee ceases to be a member of the Board of Directors of Cardinal Health (the “Cardinal Board”, and each such member, a “Cardinal Director”) by reason of Awardee’s death, any unvested portion of the CareFusion Options shall vest upon and become exercisable in full from and after Awardee’s death. The CareFusion Options may thereafter be exercised by any transferee of Awardee, if applicable, or by the legal representative of the estate or legatee of Awardee under the will of Awardee until the Grant Expiration Date.

(b) Other Termination of Service. If Awardee ceases to be a Cardinal Director for any reason other than death, any unexercised portion of the CareFusion Options which has not vested on such date of termination of service on the Cardinal Board shall automatically terminate on the date of such termination of service. Any unexercised portion of the CareFusion Options which otherwise is exercisable by Awardee (or any transferee) shall remain exercisable until the Grant Expiration Date; provided, however, that upon the removal of Awardee from the Cardinal Board for cause, other than upon or after a “change of control” (as defined in the Cardinal Health, Inc. 2005 Long-Term Incentive Plan, as amended and restated effective as of November 5, 2008), the CareFusion Options (whether then held by Awardee or any transferee) shall immediately lapse and be of no further force or effect.

4. Restrictions on Exercise. The CareFusion Options are subject to all restrictions in these Terms and/or in the Plan. As a condition of any exercise of the CareFusion Options, the Company may require Awardee or his or her transferee or successor to make any representation and warranty to comply with any Applicable Law or regulation or to confirm any factual matters (including Awardee’s compliance with the terms of paragraphs 5 and 6 of these Terms) reasonably requested by the Company. The CareFusion Options shall not be exercisable if such exercise would involve a violation of any Applicable Law.

5. Triggering Conduct/Competitor Triggering Conduct. As used in these Terms, “Triggering Conduct” shall include (i) disclosing or using in any capacity other than as necessary in the performance of duties as a Cardinal Director any confidential information, trade secrets or other business sensitive information or material concerning the Company or its subsidiaries the Cardinal Group; (ii) violating any policy of the Cardinal Group, including, but not limited to, conduct which would constitute a breach of any certificate of compliance or similar attestation/certification signed by Awardee; (iii) directly or indirectly employing, contacting concerning employment, or participating in any way in the recruitment for employment of (whether as an employee, officer, director, agent, consultant or independent contractor), any person who was or is an employee, representative, officer, or director of any entity in the Cardinal Group at any time within the twelve (12) months prior to the termination of service on the Cardinal Board; (iv) any action by Awardee and/or Awardee’s representatives that either does or could reasonably be expected to undermine, diminish or otherwise damage the relationship between the Cardinal Group and any of its customers, potential customers, vendors and/or suppliers that were known to Awardee; and (v) breaching any provision of any benefit or severance agreement with a member of the Cardinal Group. As used herein, “Competitor

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STOCK OPTIONS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

Triggering Conduct” shall include, either during Awardee’s service as a Cardinal Director or within one year following Awardee’s termination of service on the Cardinal Board, accepting employment with or serving as a consultant, advisor, or any other capacity to an entity that is in competition with the business conducted by any member of the Cardinal Group (a “Competitor”) including, but not limited to, employment or another business relationship with any Competitor if Awardee has been introduced to trade secrets, confidential information or business sensitive information during Awardee’s service as a Cardinal Director and such information would aid the Competitor because the threat of disclosure of such information is so great that, for purposes of these Terms, it must be assumed that such disclosure would occur. For purposes of these Terms, the nature and extent of Awardee’s activities, if any, disclosed to and reviewed by the Audit Committee or Nominating and Governance Committee of the Cardinal Board (each, the “Specified Committee”) prior to the date of Awardee’s termination of service on the Cardinal Board shall not, unless specified to the contrary by the Specified Committee in a written notice given to Awardee, be deemed to be Competitor Triggering Conduct. The Human Resources and Compensation Committee of the Cardinal Board (the “Cardinal Compensation Committee”) shall resolve in good faith any disputes concerning whether particular conduct constitutes Triggering Conduct or Competitor Triggering Conduct, and any such determination by the Cardinal Compensation Committee shall be conclusive and binding on all interested persons.

6. Special Forfeiture/Repayment Rules. For so long as Awardee continues as a Cardinal Director and for three years following Awardee’s termination of service on the Cardinal Board regardless of the reason, Awardee agrees not to engage in Triggering Conduct. If Awardee engages in Triggering Conduct during the time period set forth in the preceding sentence or Competitor Triggering Conduct during the applicable time periods set forth in paragraph 5, then:

(a) the CareFusion Options (or any part thereof that has not been exercised) shall immediately and automatically terminate, be forfeited, and shall cease to be exercisable at any time; and

(b) Awardee shall, within thirty (30) days following written notice from the Company, pay the Company an amount equal to the gross option gain realized or obtained by Awardee or any transferee resulting from the exercise of such CareFusion Options, measured at the date of exercise (i.e., the difference between the market value of the Shares underlying the CareFusion Options on the exercise date and the exercise price paid for such Shares underlying the CareFusion Options), with respect to any portion of the CareFusion Options that has already been exercised at any time within three (3) years prior to the Triggering Conduct (the “Look-Back Period”), less $1.00. If Awardee engages only in Competitor Triggering Conduct, then the Look-Back Period shall be shortened to exclude any period more than one (1) year prior to Awardee’s termination of service on the Cardinal Board, but include any period between the time of Awardee’s termination of service on the Cardinal Board and the time Awardee engaged in Competitor Triggering Conduct. Awardee may be released from Awardee’s obligations under this paragraph 6 if and only if the Cardinal Compensation Committee determines, in writing and in its sole discretion, that such action is in the best interests of Cardinal Health. Nothing in this paragraph 6 constitutes a so-called “noncompete” covenant. This paragraph 6 does, however, prohibit certain conduct while Awardee is associated with the Cardinal Group and thereafter and does provide for the forfeiture or repayment of the benefits granted by these Terms under certain circumstances, including, but not limited to, Awardee’s acceptance of employment with a Competitor. Awardee agrees to provide Cardinal Health with at least ten (10) days’ written notice prior to directly or indirectly accepting employment with or serving as a consultant or advisor or in any other capacity to a Competitor, and further agrees to inform any such new employer, before accepting employment, of the terms of this paragraph 6 and Awardee’s

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STOCK OPTIONS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

continuing obligations contained herein. No provisions of these Terms shall diminish, negate or otherwise impact any separate noncompete or other agreement to which Awardee may be a party, including, but not limited to, any certificate of compliance or similar attestation/certification signed by Awardee; provided, however, that to the extent that any provisions contained in any other agreement are inconsistent in any manner with the restrictions and covenants of Awardee contained in these Terms, the provisions of these Terms shall take precedence and such other inconsistent provisions shall be null and void. Awardee has acknowledged and agreed that these restrictions are for the benefit of Cardinal Health in consideration of Awardee’s receipt of the Cardinal Health Options, in consideration of exposing Awardee to Cardinal Health’s business operations and confidential information, and for other good and valuable consideration, the adequacy of which consideration is hereby expressly confirmed. Awardee has further acknowledged that the receipt of the Cardinal Health Options and the execution of the Cardinal Option Agreement were voluntary actions on the part of Awardee and that Cardinal Health would have been unwilling to provide the Cardinal Health Options to Awardee without including the restrictions and covenants of Awardee set forth above. Further, Awardee and Cardinal Health have agreed and acknowledged that the provisions contained in paragraphs 5 and 6 are ancillary to, or part of, an otherwise enforceable agreement at the time the Cardinal Option Agreement was made.

7. Change of Control. Notwithstanding anything herein to the contrary, (a) in the event a Change of Control occurs (i.e., a Change of Control occurs with respect to the Company), then the provisions of Section 16(b) of the Plan shall not apply and the CareFusion Options shall continue to vest and become exercisable in accordance with the terms set forth herein, and (b) on the date that a “change of control” (as defined in the Cardinal Health, Inc. 2005 Long-Term Incentive Plan, as amended and restated effective as of November 5, 2008) occurs with respect to Cardinal Health, any unvested CareFusion Options shall vest in full.

8. Right of Set-Off. By having accepted the Cardinal Health Options, Awardee has agreed that, so long as the amounts are not treated as “non-qualified deferred compensation” under Section 409A of the Internal Revenue Code of 1986, as amended, (a) any amounts Awardee owes from time to time to any member of the Cardinal Group with respect to the CareFusion Options may be deducted from, and set-off against, any amounts owed to Awardee by any member of the Cardinal Group from time to time (including, but not limited to, amounts owed to Awardee as director annual retainer fees, meetings fees or fringe benefits) and (b) any amounts Awardee owes from time to time to the Company or any of its Affiliates (the “CareFusion Group” with respect to the CareFusion Options may be deducted from, and set-off against, any amounts owed to Awardee by any member of the CareFusion Group from time to time (including, but not limited to, amounts owed to Awardee as director annual retainer fees, meetings fees or fringe benefits).

9. Governing Law/Venue for Dispute Resolution/Costs and Legal Fees. The CareFusion Options are governed by the laws of the State of Ohio, without regard to principles of conflicts of law, except to the extent superseded by the laws of the United States of America. Awardee has agreed that the laws of the State of Ohio bear a substantial relationship to the Cardinal Health Options and that the benefits granted therein, and thus the CareFusion Options and the benefits granted thereunder, would not be granted without their governance by the laws of the State of Ohio. In addition, all legal actions or proceedings relevant to the CareFusion Options will be brought exclusively in state or federal courts located in Franklin County, Ohio, and Awardee has consented to the personal jurisdiction of such courts. Awardee has acknowledged that the terms relating to Triggering Conduct, Competitor Triggering Conduct and special forfeiture and repayment rules set forth above are

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STOCK OPTIONS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

reasonable in nature, are fundamental for the protection of legitimate business and proprietary interests, and do not adversely affect Awardee’s ability to earn a living in any capacity that does not violate such terms. In the event of any violation by Awardee of any such covenants, immediate and irreparable injury for which there is no adequate remedy at law will result. In the event of any violation or attempted violations of these restrictions and covenants, the Cardinal Group will be entitled to specific performance and injunctive relief or other equitable relief, including the issuance ex parte of a temporary restraining order, without any showing of irreparable harm or damage, such irreparable harm being acknowledged and admitted by Awardee, waiving any requirement for the securing or posting of any bond in connection with such remedy, without prejudice to any other rights and remedies afforded the Cardinal Group hereunder or by law. In the event that it becomes necessary for the Cardinal Group to institute legal proceedings under Awardee’s CareFusion Options, Awardee will be responsible for all costs and reasonable legal fees with regard to such proceedings. Any term relating to the CareFusion Options which is determined by a court of competent jurisdiction to be invalid or unenforceable should be construed or limited in a manner that is valid and enforceable and that comes closest to the business objectives intended by such term, without invalidating or rendering unenforceable the remaining terms.

10. Action by the Administrator. Except as set forth above with respect to Triggering Conduct or Competitor Triggering Conduct, the interpretation of these Terms shall rest exclusively and completely within the sole discretion of the Administrator. Awardee shall be bound by the decisions of the Administrator with regard to the interpretation of these Terms and with regard to any and all matters set forth in these Terms. The Administrator may delegate its functions under these Terms to an officer of the CareFusion Group designated by the Administrator (hereinafter the “designee”). In fulfilling its responsibilities hereunder, the Administrator or its designee may rely upon documents, written statements of the parties or such other material as the Administrator or its designee deems appropriate.

11. Electronic Delivery and Consent to Electronic Participation. The Company may, in its sole discretion, decide to deliver any documents related to the CareFusion Options or future options that may be granted under the Plan by electronic means. Awardee has consented to receive such documents by electronic delivery and to participate in the Plan through an on-line or electronic system established and maintained by the Company or another third party designated by the Company, including the acceptance of option grants and the execution of option agreements through electronic signature.

12. Notices. All notices, requests, consents and other communications by Awardee to the Company or Cardinal Health with respect to the CareFusion Options are to be delivered in writing and will be deemed sufficient if delivered by hand, facsimile, nationally recognized overnight courier, or certified or registered mail, return receipt requested, postage prepaid, and will be effective upon delivery to the Company or Cardinal Health, as the case may be, at the address set forth below:

CareFusion Corporation

3750 Torrey View Court

San Diego, CA 92130

Attention: Compensation and Benefits Administrator

Facsimile: 858-617-2300

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STOCK OPTIONS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

Cardinal Health, Inc.

7000 Cardinal Place

Dublin, Ohio 43017

Attention: Chief Legal Officer

Facsimile: 614-757-2797

All notices, requests consents and other communications by the Company to Awardee with respect to the CareFusion Options to be delivered to Awardee may be delivered by e-mail or in writing and will be deemed sufficient if delivered by e-mail, hand, facsimile, nationally recognized overnight courier, or certified or registered mail, return receipt requested, postage prepaid, and will be effective upon delivery to Awardee.

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