If you’ve got ideas about how the Firefox home page should look, now is the time to let Mozilla know.

Mozilla is hosting a new design challenge focusing on how to improve the home tab for Firefox 4.0.

The current plan for Firefox 4.0 is to move the home button down into the tab bar as a standalone and always-accessible tab. If that’s not to your liking, you’ll still be able to disable the home tab, or simply set it to a web page as you might be doing now, but Mozilla is hoping to make the home tab a bit more powerful.

Pulling the “home” concept out of the menu bar and putting it in its own tab means that the page can access much more than just the web. It could, for example, filter through your history, add-ons, bookmarks — or pretty much anything stored in Firefox — and present that data in novel ways. What sorts of novel ways is the part that Mozilla is leaving up to you.

While some browsers are using the blank “new tab” page to display a gallery of thumbnails of favorite sites or recently visited pages — Chrome, Opera and Safari do this — the dedicated “home tab” is a new twist on browser interfaces.

One thing worth mentioning: Mozilla isn’t looking for a My Yahoo or iGoogle-style start page. That use case is pretty well covered by iGoogle and its ilk. Instead Mozilla is interested in seeing what a browser start page can do with full access to your browser.