The osteosynthesis device includes a plate for pressing against a bone and at least one threaded rod for holding the plate on the bone, the rod presenting a first thread for anchoring the rod in a bone and a second thread for co-operating with a tapped thread formed in the plate, the device being characterized in that the thread root of the second thread defines a body of cylindrical shape and in that the thread crest of the second thread defines a truncated cone.