This page has no header and no search – http://schaapwebdesign.nl/marco/test-2
If you add header image – it will not work and search will show as long as it is set to show in admin – theme options – over all header images and slider.
This is the workaround – no header + no search.
Or you disable search over header image + slider globally and you don’t need this workaround.
If you wish header + no search on 1 page only – that needs custom work and it requires a quote. Please open a ticket for that in our system here – http://support.wpestate.org/