If you don't intend on adding a logo or banner under your header navigation bar, then override the tpl_header.php file in 'includes/templates/template_default/common/' and remove everything in between the "bof-branding display/eof-branding display" comments.

Code:
<!--bof-branding display-->
<div id="logoWrapper">
    <div id="logo"><?php echo '<a href="' . HTTP_SERVER . DIR_WS_CATALOG . '">' . zen_image($template->get_template_dir(HEADER_LOGO_IMAGE, DIR_WS_TEMPLATE, $current_page_base,'images'). '/' . HEADER_LOGO_IMAGE, HEADER_ALT_TEXT) . '</a>'; ?></div>
<?php if (HEADER_SALES_TEXT != '' || (SHOW_BANNERS_GROUP_SET2 != '' && $banner = zen_banner_exists('dynamic', SHOW_BANNERS_GROUP_SET2))) { ?>
    <div id="taglineWrapper">
<?php
              if (HEADER_SALES_TEXT != '') {
?>
      <div id="tagline"><?php echo HEADER_SALES_TEXT;?></div>
<?php
              }
?>
<?php
              if (SHOW_BANNERS_GROUP_SET2 != '' && $banner = zen_banner_exists('dynamic', SHOW_BANNERS_GROUP_SET2)) {
                if ($banner->RecordCount() > 0) {
?>
      <div id="bannerTwo" class="banners"><?php echo zen_display_banner('static', $banner);?></div>
<?php
                }
              }
?>
    </div>
<?php } // no HEADER_SALES_TEXT or SHOW_BANNERS_GROUP_SET2 ?>
</div>
<br class="clearBoth" />
<!--eof-branding display-->