display custom menu on each site

Hello,

I created a custom menu called ‘mainmenu’ and insert this code to my header.php:

<?php wp_nav_menu( array( 'menu' => 'mainmenu' )); ?>

This menu appears on my main site and all sites and articles of my main blog. But when I switch to another blog of my multisite network, the menu disappears. Is it possible to display one custom menu on all multisite sites without creating the menu again and again for each blog?