For explorer this should work:

Add in the DWORD value NoSearchBox, with the value set to 1, to the following registry key:

HKEY_LOCAL_MACHINE\Software\Policies\Microsoft\Int ernet Explorer\Infodelivery\Restrictions


For Firefox

right-click magnifying glass, choose customize, now left-click and hold down the button, drag the search bar over to this window and drop it there. Now its no longer present in your browser, you can do this with Go button also if you want.

Hope this helps.