wish to change appleid on new iphone whilst keeping original id on old phone

I now have two iphones. both use same email address and apple id.My wife is to use the old one. I wish to have a new appleid on one of them whilst keeping the original on the other. how do I change the appleid on one without changing it also on the other. ? I am worried that when I change it on the new one it will also change it on the old one.