Abstract: Spinal osteosynthesis device comprising, for one and the same vertebra, a hook (12), two vertebral bearing means associated with the said hook, the latter being adapted so as to be able to bear on the median portion of the vertebral posterior arch between two longitudinal rods (7) of the said device, this hook being provided with transverse means of connection (28) between the hook and the longitudinal rods, with the possibility of adjustment, in a sagittal plane from front to back and from top to bottom, and in a frontal plane from left to right, between the rods and the said hook. The hook (12) and the two anchoring screws or hooks afford three bearing points on the same vertebra, and this avoids having to equip the stage above. Moreover, this hook can be put in place, at the end of a surgical intervention, at the desired stage and at any level chosen by the surgeon, while at the same time permitting an appreciable saving in the time taken for it to be put into place compared with the earlier systems.