Will cloning a template with a Button Generate the same Click ID?

Hi Community! I couldn’t find anything in the documentation, so I thought I’d ask here. 

When you clone an Email Template for a new program, do you have to manually re-create a button in order for a new ID to generate?

We were getting some weirdly high click through rates only to find out that the HTML in the January, June and July Buttons all had the same Click Id, which was inflating our numbers.