Abstract: This device comprises two fixation elements (4), each consisting of a hook (4) designed so as to be able to cover a rigid transverse bar (3) in a sliding manner and equipped with means (9, 8) for locking on the bar (3); this hook is made up of a body (5) and of two blades (6) spaced apart by a distance (d) of a width corresponding to that of the bar (3), and a span (7) for the hook to bear on the bar is made on the body (5) between the blades (6), which blades extend on each side of the bar when the hook straddles the latter. Two hooks (4), combined with a rectangular bar (3), form a relatively simple transverse connection device which can be positioned quickly and which has great torsional and flexural strength.