then you can deauthorize the old one. I'm not sure if you can reauthorize a computer later, though I don't see why you wouldn't be able to do that. The rules state that you can have up to 5 computers authorized at any given time.
From the iTunes help file:
You can listen to music you purchase from the iTunes Music Store on multiple computers. When you play a song you've purchased, your computer becomes "authorized" to play music purchased using your Apple or AOL account.
If the computer has not yet been authorized to play songs purchased using your account, you're asked to enter your ID and password. Enter the ID and password for the account with which the song was purchased.
Once you authorize five computers to play your music purchases, you can't listen to music you've purchased on a sixth computer until you deauthorize one of the already authorized computers. When you deauthorize a computer, you can't listen to any music that was purchased using your account on that computer. To authorize or deauthorize a computer, your computer needs to be connected to the Internet. More info is at the Apple web site:
http://www.apple.com/support/itunes/authorization.htmlYou can also contact iTunes support from the site if you can't find the answer you're looking for. :-)