styleing the wp custom-menu

Hello,

I want to get a custom structure of the menu list, created with custom-menu.

For now, I get something like this:

<div>
<ul>
<li>
<a></a>
</li>
</ul>
</div>

What I want is:

<div>
 <div>
   <ul>
    <li>
     <a></a>
    </li>
   </ul>
   <ul>
    <li>
     <a></a>
    <div>
      <ul>
       <li></li>
      </ul>
    </div>
    </li>
   </ul>
</div>
</div>

Is this possible?