The invention concerns a backbone osteosynthesis system, in particular for anterior fixing comprising: an elongated linking element; a vertebral screw with a threaded head; a connector comprising two branches capable of being engaged onto the screw and clamping between them the linking element; and a threaded clamping member capable of co-operating with the head for clamping the branches. The head has a threaded orifice, the clamping member comprising a threaded rod capable of being urged to be engaged in the orifice.