Detachable fastening system for two formwork beams, an upper beam, a lower beam, a device for connecting the upper beam to the lower beam. Said device comprises a resilient one-piece structure having two curved arms which connect zones intended to press one of said beams in support zones and zones intended to be fastened to the other beam, the system having connection means which connect the device to said beam such that it cannot be lost, and said device having the ability to slide relative to the beam to which it is fastened, the system having means for increasing the friction between the lower beam and the upper beam.