An arrangement for fastening an electrical conductor has a clamp (1) constructed as a pipe piece of metal and at least one clamping screw (2) for fastening an electrical conductor (3,4) in the clamp. The clamp has in its wall at least one throughhole provided with a thread for receiving the clamping screw. The clamping screw has a tubular contact part provided with an external thread and adapted to be screwed into the throughhole of the clamp, wherein the contact part has at its one axial end a contact surface for contacting an electrical conductor located in the clamp and along its extension with a circumferential intended breaking point a significant distance from the contact surface.