turning off "recent searches"?

I've set up a search function with a dropdown menu, from a script I found online. But I have an unexpected problem. When somebody goes to type in the box, my dropdown appears to filter their search (just as I want), but the browser's "recent searches" dropdown appears over it.

Is it possible to control where this appears, how many recent searched terms appear, etc?

Should do the trick.

https://developer.mozilla.org/En/How_to_Turn_Off_Form_Autocompletion