A plate is provided with clearance holes and fastening screws. Each screw is provided in the region of its head with a clamping part subdivided into tongues by means of slots and provided with an internal opening bounded by a conical surface. To each screw belongs an expander having a conical outer surface. The expander is axially displaceable in relation to the clamping part to force the tongues of the clamping part apart and lock the screw in relation to the plate. A rigid connection between the plate and the screws is thus provided, even if reabsorption of bone material takes place at the bearing surface of the plate.