A transverse spinal linking device links at least one spinal osteosynthesis bar to a transverse bar. The device may include a first part that has a vertical axis and a first jaw, a second part that has a second jaw, and a clamping resource. The first part may include a sliding surface, which may be inclined in relation to the vertical axis, and which may mate with at least one sliding surface of the second part. The sliding surfaces may be configured so that the descent of the second part results in an approach of the jaws, with the clamping action of the clamping resource causing the fixing and/or the locking of the device on the osteosynthesis bar and the fixing and/or the locking of the transverse bar.