How to create a navigation from sub-categories?

I’m trying to create a secondary navigation which ‘pulls’ links for all sub categories within a parent.

For each link I need the code to be in this structure (due to the way the page is styled):

<li><a class="guide-button" href="[sub-cat-link]"><span>[sub-cat-title]</span></a></li>

Is there any way to create some code that would get all sub-categories and use the above structure?

Many thanks.