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The Cupertino, Calif., Mac maker initiated the program on Friday. Affected iMac owners who provided an email during the product registration process are being contacted regarding the issue.
"Apple has determined that a very small number of Seagate 1TB hard drives used in 21.5-inch and 27-inch iMac systems, may fail under certain conditions. These systems were sold between May 2011 and July 2011," the company said.
Users who have not received an email from Apple can check the program's webpage to see if they are eligible for the replacement.
The company offers three options for replacing the hard drives: Apple Retail Store, Apple Authorized Service Provider and Apple Technical Support.
Apple recommends that customers take advantage of the replacement "as soon as possible." Customers are also advised to back up their data prior to going in for service. They will also need to have the original OS installation discs that shipped with their product in order to reinstall the "operating system, other applications and any backed up data after your hard drive is replaced."
The program will run through July 23, 2012, at which time Apple will evaluate whether further extensions are needed. The recall does not extend the standard warranty coverage of the iMac.
Apple released the current generation of iMacs in May, adding quad-core Sandy Bridge processors from Intel and the high-speed Thunderbolt input/output port. 1TB hard drives come standard on all but the entry-level model.