That is not a border. It is an IE bug, and the standard fix is to edit /includes/templates/your_template/common/tpl_header.php. Find this at the end of the branding display section:
PHP Code:
<br class="clearBoth" />
<!--
eof-branding display--> 
Replace the
<br class="clearBoth" />
with
<div class="clearBoth" /></div>