The invention relates to a rail fastening on a tie having fastening screws and loop-shaped tension clamps in which the track width can be adjusted horizontally in a stepless manner using wedge elements, the rail being arranged on a ribbed plate, the ribs of which run at an angle to the rail and a wedge that can be moved in the longitudinal direction of the rail being arranged between rail foot and the ribs. The wedge is preferably guided on the support. This makes possible effective horizontal lateral displacement of the rail or modification of the track with the use of simple and inexpensive plastic parts.