Abstract: The invention relates to a sequential connection device for connecting together a rod and a screw head having spherical symmetry. The device comprises a first longitudinal part and second longitudinal part suitable for co-operating together. Said first first end presenting a top portion and a curved bottom portion facing said top portion, said bottom portion presenting bottom bearing points against which said screw head can come to bear. Said top portion includes an adjustable thrust disposed facing said bottom portion and spaced apart from said screw head, the adjustable thrust and said bottom bearing point defining a polyhedron inside which the center C of said screw head can be situated.