Is that in the google toolbar? If yes then goto the options for the toolbar and under the search tab uncheck the first checkbox which says "Save the serach history".
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Microsoft Internet Explorer
1. Go to the "Tools" menu.
2. Select "Internet Options" and the "Content" tab.
3. Within the "Personal information" area, select "AutoComplete."
4. Click on "Clear Forms." You can also un-check the "Forms" box in this window to keep this information from being stored in the future.
5. Click "OK" to exit.
Alternatively, you can delete individual entries from your search history by using the Down arrow key to highlight a previous search, then pressing the Delete key once.
Sorry if the idea was repeated... but its for ppl like me who love the step by step procedure...