Remove Item from Navigation menu

I am trying to remove from my home navigation menu the 'small' search icon (the magnify glass icon)....I have already removed the search button for guests  and that works fine.... but I cannot seem to figure out how to remove this second small search  nav. menu item...Can anyone tell me how to do this???

I am also trying to find how to remove this if anyone can help, thanks, Ron

open "templates/base/scripts/BxBaseMenu.php" file

find below

$aFunctions = array('genMoreLanguagesElement', 'genMoreTemplatesElement', 'genSearchElement');

and remove the last element ('genSearchElement') from the array