Changing the site URL to registered domain

Hi,

Apologies in advance but this may be a stupid question.

I have a WP install in a subfolder on my server http://www.beardedonline.com/blog.
I have a registered domain http://www.me.com

I want the WP install to stay where it is on the server, but I want the URL to look like it’s a subdomain of me.com.

For example, a post might have the physical URL of http://www.beardedonline.com/blog/post, but I want the user to see http://www.me.com/post

I’ve read this page on changing the site URL but the domain me.com is registered elsewhere.

Do I have to move the registered domain name to the same server, or is it possible to use this domain name to be the prefix to all my posts?

Hopefully that’s clear, any help greatly appreciated.

Thanks!