Exhibit 10.5.5

RSUS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

ADJUSTMENTS TO CARDINAL HEALTH RESTRICTED SHARE UNITS AND TERMS OF

CAREFUSION RESTRICTED SHARE UNITS

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 restricted share unit awards granted by Cardinal Health to you (the “Cardinal Health RSUs”) pursuant to the terms of equity incentive plans adopted by Cardinal Health (“Cardinal Health Equity Plans”), and related grant agreements (the “Cardinal Health RSU Agreements”) are being adjusted, as of the effective time of the Spin-Off, as follows:

Pre-2007 Cardinal RSUs and Adjusted Post-2007 Cardinal RSUs

Except for the adjusted number of shares subject to each Adjusted Post-2007 Cardinal RSU, your Pre-2007 Cardinal RSUs and Adjusted Post-2007 Cardinal RSUs will continue to be governed by (i) your Cardinal Health RSU 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 Plans. Therefore, among other terms, the extent to which each Pre-2007 Cardinal RSU and Adjusted Post-2007 Cardinal RSU will vest on and after specific dates will be the same as those set forth in your Cardinal Health RSU Agreements.

RSUS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

The adjusted number of shares subject to each Adjusted Post-2007 Cardinal RSU 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 Pre-2007 Cardinal RSUs and Adjusted Post-2007 Cardinal RSUs and as a result CareFusion may enforce with full force and effect all terms and conditions that benefit CareFusion with respect to such RSUs.

CareFusion RSUs

Your CareFusion RSUs 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 Health RSU Agreement for the corresponding Cardinal Health RSU (including paragraphs 3 and 4 of the agreement 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 RSUs 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 RSUs 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 RSUs.

RSUS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

Appendix A

CAREFUSION CORPORATION

RESTRICTED SHARE UNITS TERMS AND CONDITIONS

These Restricted Share Units Terms and Conditions (the “Terms”) adjust and restate the terms that apply to the Cardinal Health RSUs (as defined below) for purposes of applying such terms to the restricted share units (the “CareFusion RSUs”) 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 RSU Terms (as defined below) and the Plan, shall govern the CareFusion RSUs. The CareFusion RSUs are Replacement Awards under the Plan.

The “Number of Shares” that are covered by the CareFusion RSUs constitute the RSU terms (the “RSU Terms”) and can be found on the website of the Company’s third-party equity plan administrator. The extent to which the CareFusion RSUs shall vest 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”), is the same as set forth in Awardee’s award agreement (the “Cardinal Health RSU Agreement”) for the restricted share units granted to Awardee by Cardinal Health (the “Cardinal Health RSUs”) on the grant date specified in the Cardinal Health RSU Agreement (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. Transferability. The CareFusion RSUs shall not be transferable.

2. Termination of Service on the Board. 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”) prior to the vesting in full of the CareFusion RSUs for any reason other than Awardee’s death, all of the then unvested CareFusion RSUs shall be forfeited by Awardee. If Awardee ceases to be a member of the Cardinal Board prior to the vesting of the CareFusion RSUs by reason of Awardee’s death, then such CareFusion RSUs shall immediately vest in full and not be forfeited.

3. 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 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

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RSUS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

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 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.

4. 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 3, then:

(a) the CareFusion RSUs that have not yet vested or that vested within the Look-Back Period (as defined below) with respect to such Triggering Conduct or Competitor Triggering Conduct and have not yet been settled by a payment pursuant to paragraph 6 hereof shall immediately and automatically terminate, be forfeited, and shall cease to exist; and

(b) Awardee shall, within thirty (30) days following written notice from the Company, pay to the Company an amount equal to (i) the aggregate gross gain realized or obtained by Awardee resulting from the settlement of all CareFusion RSUs pursuant to paragraph 6 hereof measured as of the settlement date (i.e., the market value of the CareFusion RSUs on such settlement date), that have already been settled and that had vested at any time within three (3) years prior to the Triggering Conduct (the “Look-Back Period”), minus (ii) $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 4 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 4 constitutes a so-called “noncompete” covenant. This paragraph 4 does, however, prohibit certain conduct while Awardee is associated with the Cardinal Group and thereafter and does provide for the forfeiture

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RSUS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

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 4 and Awardee’s 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 RSUs, 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 RSUs and the execution of the Cardinal Health RSU Agreements were voluntary actions on the part of Awardee and that Cardinal Health would have been unwilling to provide the Cardinal Health RSUs 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 3 and 4 are ancillary to, or part of, an otherwise enforceable agreement at the time the Cardinal Health RSU Agreements were made.

5. 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 RSUs shall continue to vest 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, the restrictions applicable to any unvested CareFusion RSUs shall lapse and the Award shall be fully vested.

6. Payment. Awardee will be entitled to receive from the Company the Shares represented by such CareFusion RSUs at the same time as Awardee is or would have been entitled to receive Cardinal Health common shares represented by the Cardinal Health RSUs.

7. Dividend Equivalents. Awardee shall not receive cash dividends on the CareFusion RSUs, but instead shall, with respect to each CareFusion RSU, receive a cash payment from the Company on each cash dividend payment date with respect to the Shares with a record date between the effective time of the Spin-Off and the settlement of such unit pursuant to paragraph 6, with such cash payment to be in an amount equal to the dividend that would have been paid on the Common Share represented by such unit. Cash payments on each cash dividend payment date with respect to the Shares with a record date prior to a Vesting Date shall be accrued until the Vesting Date and paid thereon (subject to the same vesting requirements as the underlying CareFusion RSUs). In addition, if (a) the CareFusion RSUs replace one or more Cardinal Health RSUs that were canceled and (b) Awardee was entitled to one or more cash dividend equivalent payments under the Cardinal Health RSUs that had not been paid prior to the effective time of the Spin-Off because the Cardinal Health RSUs had not yet vested, then the Company shall pay such cash payments on the Vesting Date.

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RSUS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

8. Right of Set-Off. By having accepted the Cardinal Health RSUs, 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 RSUs 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, meeting 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 RSUs 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, meeting fees or fringe benefits).

9. No Stockholder Rights. Awardee shall have no rights of a stockholder with respect to the CareFusion RSUs, including, without limitation, the right to vote the Shares represented by the CareFusion RSUs.

10. Governing Law/Venue for Dispute Resolution/Costs and Legal Fees. The CareFusion RSUs 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 RSUs and that the benefits granted therein, and thus the CareFusion RSUs 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 RSUs 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 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 RSUs, Awardee will be responsible for all costs and reasonable legal fees with regard to such proceedings. Any term relating to the CareFusion RSUs 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.

11. 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

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RSUS

(NON-EMPLOYEE DIRECTORS (CURRENT AND FORMER))

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.

12. Electronic Delivery and Consent to Electronic Participation. The Company may, in its sole discretion, decide to deliver any documents related to the CareFusion RSUs or future RSUs 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 RSU grants and the execution of RSU agreements through electronic signature.

13. Notices. All notices, requests, consents and other communications by Awardee to the Company or Cardinal Health with respect to the CareFusion RSUs 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

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 RSUs 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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