Another install

I have Norton on this machine.  I bought another machine with Norton on it.  Is is a trial for 60 days.  I will replace it with the copy  of Norton I have already purchased for this machine.  I can load it on 3 machines.  I am assuming that I have to uninstall the new one before I install my purchased copy on the new machine.  Is that correct or can I just re- register the copy on my new machine to my original purchased copy. 

 

Thanks