Bet Angel is licensed by username so you can install a copy on as many computers as you wish once you have initially registered the serial number.
There is no need to re-register Bet Angel and you do not need a new serial number just visit the download page, download the latest version and install. Then just log in and use as normal.
You may also open multiple instances on the same computer with the same username, to do so just click the Bet Angel icon again to repeat the usual log in process.
Bet Angel Support