Updating Version 3.2.1 to 4.1

We just took on a new client and their site is currently version 3.2.1! Obviously, we want to update but it’s timing out whenever we try.

Would we want to do this manually here: http://codex.ww.wp.xz.cn/Updating_WordPress#Manual_Update or would there be a separate step we should look at with such a jump in versions?