Delete a FaceTime contact on your Mac to prevent someone from contacting you. Like Skype and Windows Live Messenger, FaceTime allows you to add people to your contact list using email addresses. Unlike these other two programs, however, it isn't possible to "block" someone from communicating with you. Rather, FaceTime prohibits anyone who isn't on your contact list from communicating with you.
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Launch FaceTime on your Mac. Sign in using your Apple ID and your password. Your Apple ID is the same email address you use to make purchases on iTunes.
Click the name of a contact within your contact list. Choose the "Edit" button in the top right corner of the window.
Scroll to the bottom of the contact's entry. Click the red "Delete Contact" button to remove the person from your contact list.