Fastening of rails on wooden or concrete sleepers by a metal pressure plate-clip in the form of a trapezoid (1.5) and a plastic tie-plate (1.4). The metal pressure plate-clip and the plastic tie-plate constitute an entirety, and provides a continuous pressure along its entire edge (2.1). The edge leaning on the rail base is formed in the way to enable a smooth gliding along the rail base during pulling on, preventing unnecessary resistance and damage. The other, narrower side of the pressure plate is formed in the way that it has a fixation edge at its end (3.2), preventing any shifting. The plastic tie-plate has a fixation groove at its outer end (4.2) in which the narrower, outer end of the pressure plate enters. The groove is formed in the way that it forms a firm connection with the outer end of the metal pressure plate-clip, so that taking out of the pressure plate is not possible. The tie-plate also contains a bigger groove (4.4), which allows deformation of the pressure plate during dismounting.