If you're referring to the box into which you type search terms shown in your attachment, and if you're using Internet Explorer, to clear them all at once, go to IE's Tools>Internet Options>Content tab>Auto Complete button and uncheck "Forms," click OK. If that's left unchecked, it will not remember anything typed into any form field in the future...including ones like the one in your attachment.
If you want to clear them individually, double click on the search box then use the down arrow to select and the delete key to delete entries.
Ooops....Statica's reply didn't load the first time around so I didn't see it but, hey, at least we agree.
