To cancel the authorization of Spine on your previous computer, you can simply log out of Spine on that computer. This can be done by going to the Settings menu (click the Spine logo in the top left or press F12) and selecting "Log Out" at the bottom left. Once logged out, you can then install and activate Spine on your new computer using your license. If you didn't log out, the Spine license system will automatically log out the old computer when you activate Spine on a new computer.