Vertebral osteosynthesis equipment includes bony anchoring members, such as pedicular screws or hooks, at least one of which includes a proximal threaded stud for receiving a nut and a base portion for anchoring to a vertebra linking rods, intended to be connected to these anchoring members and attached to the vertebrae by these anchoring members, parts for connecting these linking rods to the anchoring members, and extension pieces for engaging on the proximal stud(s) of the anchoring member(s) for running down connecting parts on this or these proximal stud(s) until they rest on the proximal zone(s) of the base portion(s) of the anchoring members. The proximal stud of at least one anchoring member and the extension piece intended to be used with this anchoring member include positioning elements for positioning the extension piece on the free end of the proximal stud, concentrically thereto.
