The answers I have found tells you how to delete the search history AND to clear the forms, but I don't want that:
"Open the Mozilla Firefox browser, select "Tools" in the upper left-hand menu and select the "Clear Recent History" option. Tick the "Form & Search History" box and click the "Clear Now" button to delete Firefox's search history. Please note that you cannot undo this action."
I want to clear ONLY the search history.