If the new PC is running XP or Vista, yes.
Simply uninstall Onecare on the old PC and install on the new PC -
http://onecare.live.com, Member Accounts, Add a computer. After it is installed, activate with the LiveID for your subscription (found in Help/About in OneCare on the existing PC).
Note that removing OneCare is optional as you are allowed to have 3 PCs using the same LiveID/Subscription.
If the new PC is running Windows 7:
Installation of Windows Live OneCare in Windows 7 is not supported. You can use the free Microsoft Security essentials for malware protection - http://www.microsoft.com/security_essentials/resources.aspx
See this post for End of Life information for Windows Live OneCare - http://social.microsoft.com/Forums/en-US/onecaregeneral/thread/81996436-edad-41ba-bdfc-02fc094e2ca9
-steve
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