The instrumentation comprises for each lumbar vertebra (L5), two pedicular screws (1) having two screw threads (9, 11), one (9) of the screw threads corresponding to the region of penetration of the screw in the pedicle, two rods (2) having asperities respectively associated with a pedicular screw and secured to the latter by connection elements (3) provided with elements for clamping the rods. Each connection element (3) is in one piece and the screw thread (9) corresponding to the region of penetration of the screw in the pedicle terminates in an annular shoulder (16) against which the connection element bears which is separated by a smooth part (15) from the screw thread (11) outside the region of penetration in the pedicle. This instrumentation permits both returning the slipped vertebrae rearwardly and pivoting it in the desired direction of rotation, it being possible to carry out the derotation action slowly and by controlling the movement so that the surgeon achieves on the whole in the two movements an excellent precision in the repositioning of the vertebrae relative to the neighbouring vertebrae.