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As has been said, yes you can, but you would have had to save the license file so you can use it again.

If you don’t save it you can use the Resend avast License http://www.avast.com/resend-license-paid.php, you will need to enter the email that you used when purchasing the license, e.g. the one that the original email with the link was sent.

Always best to keep a copy of the license file of the system.