A system for forming a flooring includes rectangular floorboards (1, 1′) including first and second types of floorboards (A, B), on which first and second locking devices are arranged in pairs on opposing short edges (5a, 5b) and long edges (4a, 4b), respectively, and on which the locking device of the first type of floorboard (A) along one pair of opposing joint edges is mirror inverted relative to the corresponding locking device along the same pair of opposing joint edges of the second type of floorboard (B). The system includes a third type of floorboard (C), which is so designed that a first one (5b) of its two short edges presents the first locking device (12) and both its long edges (4a, 4b) and its other short edge (5a) presents the second locking device.