Exhibit 99.1

ResMed Announces Early Redemption of 4% Convertible Notes

SAN DIEGO, California, January 5, 2006 – ResMed Inc (NYSE: RMD) today announced that it has exercised its right to call for an early redemption of all of its outstanding 4% convertible subordinated notes due June 20, 2006. Convertible notes in an aggregate principal amount of $113.25 million are currently outstanding. The redemption price is approximately $1,016 per $1,000 principal amount of notes, including accrued interest through the early redemption date of March 3, 2006.

Note holders may elect to convert the notes into ResMed shares of common stock at any time until 5:00 PM Eastern Time on Thursday, March 2, 2006. The notes are convertible into approximately 33 ResMed shares for each $1,000 principal amount of bonds, at a conversion price of $30.30 per share. No payment will be made for accrued interest on notes surrendered for conversion.

ResMed would issue an aggregate of approximately 3.74 million shares if all currently outstanding notes were converted. The dilutive impact of these conversions has already been reflected in ResMed’s reported diluted net income per share in accordance with US generally accepted accounting principles.

For assistance with redemption or conversion, please contact American Stock Transfer Shareholder Services at (800) 937-5449.

About ResMed

ResMed is a leading manufacturer of medical equipment for the treatment and management of sleep-disordered breathing and other respiratory disorders. We are dedicated to developing innovative products to improve the lives of those who suffer from these conditions and to increasing awareness among patients and healthcare professionals of the potentially serious health consequences of untreated sleep-disordered breathing. For more information on ResMed, visit www.resmed.com.

Contact:

Hillary Theakston

Director of Investor Relations

(858) 746-2610

hillaryt@resmed.com