Index: wp-includes/theme.php
===================================================================
--- wp-includes/theme.php	(revision 11812)
+++ wp-includes/theme.php	(working copy)
@@ -600,7 +600,18 @@
  * @return string
  */
 function get_category_template() {
-	$template = locate_template(array("category-" . absint( get_query_var('cat') ) . '.php', 'category.php'));
+	$cat_ID = absint( get_query_var('cat') );
+
+	$category = get_category( $cat_ID );
+	if ( is_wp_error( $category ) )
+		return false;
+
+	$template = locate_template(array(
+		"category-" . $category->slug . '.php',
+		"category-" . $cat_ID . '.php',
+		'category.php'
+	));
+
 	return apply_filters('category_template', $template);
 }