That would require a template edit.
Template: header
Find:
PHP Code:
<vb:if condition="$show['registerbutton']">
<li><a href="register.php{vb:raw session.sessionurl_q}" rel="nofollow">{vb:rawphrase register}</a></li>
</vb:if>
Change it to:
PHP Code:
<!-- <vb:if condition="$show['registerbutton']">
<li><a href="register.php{vb:raw session.sessionurl_q}" rel="nofollow">{vb:rawphrase register}</a></li>
</vb:if> -->
The <!-- and --> around the code makes it so that the code will be ignored. I wouldn't suggest in removing it, just in case you might wish to re-add it later on. If that is the case in the future, just remove the <!-- in the beginning and --> at the end.