A system for fastening a rail includes a sleeper having a supporting face supporting the flange of the rail and merging at its sides into respective levelling faces situated at a higher level than the supporting face, an angled mounting plate having a central portion on the underside of which is formed a support surface by which the angled mounting plate can be placed down on the respective levelling face assigned thereto, a supporting portion formed onto the central portion and pointing downwards from the underside of the latter and which can bridge a clear space between the flange of the rail and the levelling face, a resilient member which can be placed down on the angled plate and has two holding arms by which the resilient member can exert a holding force on the rail, and a clamping member which can exert a clamping force on the resilient member.