A device for removably securing the edge, provided with a profiling, of a floor covering to a profile construction delimiting the floor covering, the profile construction being in particular a step nosing profile with an angular step profile and a base profile which can be secured on a step and the angular step profile having a step leg with a covering wing and a stop leg, wherein an interchangeable insert which is configured as a profile rail and is arranged such that it can be removed and can be adapted in its position to the profile construction and on which is configured, at least on one of its two mutually opposite longitudinal edges, a retainer which cooperates with the profiling of the edge of the floor covering and is configured to be at least partly complementary to the profiling.