Exhibit 31.4

CERTIFICATION BY THE CHIEF FINANCIAL OFFICER

PURSUANT TO 17 CFR 240.13a-14(a)/15d-14(a)

AS ADOPTED PURSUANT TO

SECTION 302 OF THE SARBANES-OXLEY ACT OF 2002

I, Charles J. Dockendorff, certify that:

(1) I have reviewed this Amendment No. 1 to the annual report on Form 10-K of Covidien plc;

(2) Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report.