Abstract: The ostheosynthesis connection device of the invention is designed to connect a screw for implanting in the spine to a vertebral support rod. The screw is constituted by a bottom first threaded portion, a head having flats and a curved base, and a top second threaded portion in line with the first. A nut having a curved base is suitable for co-operating with the second threaded portion. For connection with the screw, a connection piece has a hole of inside diameter that is greater than the outside diameter of the second threaded portion of the screw, and around said hole it has curved top and bottom bearing faces such that the connection piece is locked in position relative to the screw once the nut has been tightened by the curved base of the nut bearing against the top bearing face thereof and by the bottom bearing face being clamped against the curved base of the head of the screw.