A system for fastening a rail having a rail foot, a web positioned thereon, and a rail head, includes a tensioning clamp with a carrying plate. The carrying plate has a central portion for bracing the tensioning clamp on the carrying plate, at least one torsion portion branching off from the central portion in the lateral direction and a holding arm connected to the torsion portion via a curved transition portion. The holding arm extends, starting from the transition portion, counter to the torsion portion and exerts via the free end of its end portion a resilient holding-down force on the rail foot of the rail to be fastened. The length of the torsion portion and the course of the transition portion is adapted to each other in such a way that at least the transition portion is guided without supports laterally past a region of the carrying plate that is associated with the central portion of the tensioning clamp. The end portion of the holding arm is angled away from the torsion portion in such a way that it points in the direction of the web of the rail to be fastened.