The invention relates to a connection system (3, 12, 13) between two longitudinal cylindrical spinal support rods (4), said connection system comprising at least one transverse elongate element (6, 14) having, on each end thereof, a head (7, 8 17, 18 43) for attaching onto a corresponding rod. At least one of said attachment heads (7, 8 17, 18) includes a semi-cylindrical recess (19) for clipping with the rod (4), said recess having an upper lip (20, 21), covering the bottom of the rod, and a lower lip (22, 23), that is radially opposite said upper lip, and the head comprises a means (11, 24) for bending said lower lip (22, 23) between a position for connecting and a position for locking onto the rod.
