Hi

What about a master page for public site of SharePoint online (part of the Office 365) ?

I am trying now to make a new one but it's hard to understand the mechanism.

Thank's

Actually no, the public sites for SharePoint online are a completely different mechanism. You are not supposed to edit master pages (in fact I broke mine pretty good trying :) Instead you are just overriding CSS and the HTML classes are completely different from the traditional SharePoint HTML markup. In some ways it is easier. I suggest using Firebug and IE Dev Tools to understand the CSS.