Abstract: A vertebral osteosynthesis device employs outside faces of lateral walls of each hooking element which are inclined toward each other such that they converge from the side opposite hooking elements designed to be attached to the bone, while a gripping element in the shape of a clamp has side arms with inside faces inclined at slopes that match those of outside faces of lateral walls. At least two gripping means are disposed beyond the lateral walls and are provided to move the gripping element such that the inside faces of its lateral arms abut the lateral walls, bringing them toward each other and sliding on them upon gripping, to bring the lateral walls closer together to lock each hooking element onto a support rod.