Fastening strap composed of a rod having a vertical rectilinear part (20) and a curved part which forms a spring and the end (10) of which grips the flange (25) of the rail to be fastened, after being tensioned as a result of the rotation of the strap above a ramp (30), the lower end of the rectilinear part being equipped with a heel (2) catching on a retaining surface (36) in the tie. The strap has an intermediate bearing point (6) which, during the rotation of the strap, bears on an abutment (38) or on a bearing surface of a metal sole plate. This intermediate bearing point ensures the stability of the strap during its rotation and in its tensioned position and, if an abutment is used, keeps this abutment in place.