Index: wp-includes/formatting.php
===================================================================
--- wp-includes/formatting.php	(revision 43896)
+++ wp-includes/formatting.php	(working copy)
@@ -2780,10 +2780,18 @@
  * @return string Converted content.
  */
 function wp_targeted_link_rel( $text ) {
+  
+  $original_text = $text;
+  
 	// Don't run (more expensive) regex if no links with targets.
 	if ( stripos( $text, 'target' ) !== false && stripos( $text, '<a ' ) !== false ) {
 		$text = preg_replace_callback( '|<a\s([^>]*target\s*=[^>]*)>|i', 'wp_targeted_link_rel_callback', $text );
 	}
+  
+  // Return original link from wp_targeted_link_rel_callback after applying wp_targeted_link_rel if rel is empty.
+  if ( strpos( $text, 'rel=""' ) !== false ) {
+    return $original_text;
+  }
 
 	return $text;
 }