The reason that search boxes hold information is because your browser is set to save information that is entered on forms. You can turn this setting off by going to tools and options for your browser. In the content tab (or privacy tab in some browsers) you can adjust this setting. If the browser is not storing the information but there is an installed toolbar that is holding your search information try finding the options icon which may be a small arrow on the toolbar itself. You can make the adjustment to the toolbar in this manner to clear the search history and stop it from saving your searches.