Exhibit 10.2.4

THIRD AMENDMENT TO THE CARDINAL HEALTH, INC. 2005 LONG-TERM INCENTIVE PLAN, AS
AMENDED AND RESTATED AS OF NOVEMBER 5, 2008

This Third Amendment to the Cardinal Health, Inc. 2005 Long-Term Incentive Plan,
as amended and restated as of November 5, 2008 (the “Plan”), is effective as of
May 6, 2014, pursuant to resolutions of the Human Resources and Compensation
Committee of the Board of Directors of Cardinal Health, Inc., adopted during a
meeting held on May 6, 2014.

1. The first sentence of Subsection (ll) of Section 2 of the Plan is hereby
deleted in its entirety and in replacement thereof shall be the following:

““Termination of Employment” means, unless otherwise provided in an Award
Agreement, ceasing to be an Employee; provided, however, that, unless otherwise
determined by the Administrator, for purposes of this Plan, a Participant will
not be deemed to have had a Termination of Employment if such Participant
continues to be or becomes a Director or becomes an independent contractor,
leased employee or consultant to the Company.”