EXHIBIT 23.1

INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM’S REPORT ON SCHEDULE AND CONSENT

The Board of Directors and Stockholders

ResMed Inc:

The audits referred to in our report dated August 13, 2004, included the related financial statement schedule as of June 30, 2004 and for each of the years in the three-year period ended June 30, 2004. This financial statement schedule is the responsibility of the Company’s management. Our responsibility is to express an opinion on this financial statement schedule based on our audits. In our opinion, such financial statement schedule, when considered in relation to the basic consolidated financial statements taken as a whole, presents fairly in all material respects the information set forth therein.

Our report refers to a change in the method of accounting for goodwill in 2002.

We consent to incorporation by reference in the registration statements (Nos. 333-08013, 333-88231 and 333-115048) on Form S-8 and the registration statements (Nos. 333-70500 and 333-100825) on Form S-3 of ResMed Inc. of our reports included herein.

/s/ KPMG LLP

San Diego, California

August 27, 2004