If I remove 360 from one PC can I install it on a different one?

Hi, I have a Norton 360 subscription that is good for use on 3 separate PCs. I recently bought a new laptop and my old one has 360 installed on it, as does my home PC and my sister's laptop, so my question is, if I remove Norton 360 from my old laptop, will that allow me to reinstall it on my new one with my current subscription?