The ground air traffic controller gave the pilots the instruction to line up on runway 04 and taxi to intersection Foxtrot. The pilots taxied to the beginning of runway 04 where they made a turn of 180 degrees near intersection Foxtrot and prepared the aircraft for departure. The pilots performed the ‘before take-off’ checklist and subsequently took off on the assumption that they had received the take off clearance. During the climb the air traffic controller reported that he had not given the clearance yet to take off and expected that the aircraft would have left the runway near intersection Foxtrot. There was no risk of a collision with other aircraft.