In general, it is recommended that you format your drive and re-install the system software before you sell your computer.

Uninstall Live on the PC or delete the Live application folder on the Mac. You will also need to delete the Unlock.cfg file. The Unlock.cfg file is located in the following paths:

Windows (Live 3): (Installation Directory)/Ableton/Unlock
Windows (Live 4 and 5): C:\Documents and Settings\your user name\Application Data\Ableton\Live 4\Unlock
Mac OS 9: /System/Application Support/Ableton/Unlock
Mac OS X: /User/Library/Application Support/Ableton/Unlock
Note that on some Windows systems the application data folder is hidden by default. Here is how to make it visible:

Windows XP/2000

Launch Explorer.
Select Tools/Folder Options/View.
Check "Show hidden files and folders."