Index: src/wp-admin/includes/update.php
===================================================================
--- src/wp-admin/includes/update.php	(revision 25998)
+++ src/wp-admin/includes/update.php	(working copy)
@@ -209,6 +209,10 @@
 	if ( ! isset( $cur->response ) || $cur->response != 'upgrade' )
 		return false;
 
+	// Make sure the site admin update notice won't be displayed too.
+	remove_action( 'admin_notices', 'site_admin_notice' );
+	remove_action( 'network_admin_notices', 'site_admin_notice' );
+
 	if ( current_user_can('update_core') ) {
 		$msg = sprintf( __('<a href="http://codex.wordpress.org/Version_%1$s">WordPress %1$s</a> is available! <a href="%2$s">Please update now</a>.'), $cur->current, network_admin_url( 'update-core.php' ) );
 	} else {