How to remove the home link in menu breadcrumb in drupal
You can check if your theme bring this option in appearance > Theme settings

Or you'll have to use THEME_breadcrumb hook. Here's the zen function, have a look at the bolded part.

function zen_breadcrumb($variables) {
  $breadcrumb = $variables['breadcrumb'];
  $output = '';

  // Determine if we are to display the breadcrumb.
  $show_breadcrumb = theme_get_setting('zen_breadcrumb');
  if ($show_breadcrumb == 'yes' || $show_breadcrumb == 'admin' &amp;&amp; arg(0) == 'admin') {

    // Optionally get rid of the homepage link.
    $show_breadcrumb_home = theme_get_setting('zen_breadcrumb_home');
    if (!$show_breadcrumb_home) {
      array_shift($breadcrumb);
    }

    // Return the breadcrumb with separators.
    if (!empty($breadcrumb)) {
      $breadcrumb_separator = theme_get_setting('zen_breadcrumb_separator');
      $trailing_separator = $title = '';
      if (theme_get_setting('zen_breadcrumb_title')) {
        $item = menu_get_item();
        if (!empty($item['tab_parent'])) {
          // If we are on a non-default tab, use the tab's title.
          $breadcrumb[] = check_plain($item['title']);
        }
        else {
          $breadcrumb[] = drupal_get_title();
        }
      }
      elseif (theme_get_setting('zen_breadcrumb_trailing')) {
        $trailing_separator = $breadcrumb_separator;
      }

      // Provide a navigational heading to give context for breadcrumb links to
      // screen-reader users.
      if (empty($variables['title'])) {
        $variables['title'] = t('You are here');
      }
      // Unless overridden by a preprocess function, make the heading invisible.
      if (!isset($variables['title_attributes_array']['class'])) {
        $variables['title_attributes_array']['class'][] = 'element-invisible';
      }

      // Build the breadcrumb trail.
      $output = '&lt;nav class="breadcrumb" role="navigation"&gt;';
      $output .= '&lt;h2' . drupal_attributes($variables['title_attributes_array']) . '&gt;' . $variables['title'] . '&lt;/h2&gt;';
      $output .= '&lt;ol&gt;&lt;li&gt;' . implode($breadcrumb_separator . '&lt;/li&gt;&lt;li&gt;', $breadcrumb) . $trailing_separator . '&lt;/li&gt;&lt;/ol&gt;';
      $output .= '&lt;/nav&gt;';
    }
  }

  return $output;
}


Zen provide an option to disable this feature :

$show_breadcrumb_home = theme_get_setting('zen_breadcrumb_home');
if (!$show_breadcrumb_home) {
  array_shift($breadcrumb);
}