Show first child of element without a specific class using jQuery

I am trying to show the first child of an element which does not have a class of "submitted"

So something like

$('#menu li:first-child:not(".submitted")').show();

HTML:

<ul id="menu">
   <li class="submitted">stuff here</li>
   <li class="submitted">stuff here</li>
   <li>stuff here</li> <!-- This one needs to be shown -->
   <li>stuff here</li>
   <li>stuff here</li>
</ul>

Any ideas??