A removable covering for surfaces includes, in principle, tiles consisting of bases made of a plastic material and top plaques joined to the bases, the bases incorporating male and female anchoring elements along their edges which fit together for attaching one tile to another. The anchoring elements are located in the joints between tiles and the anchoring elements are arranged alternatingly along the entire outer edge of the bases, at least by pairs of anchoring elements, one male and the other female, on each side of the edge of the plastic base. The anchoring elements are separated by a distance which is twice the distance between each end anchoring element and the nearest adjacent vertex of the corresponding base. It will thus be possible to place and anchor one tile assembly in relation to another in as many positions as the number of sides of the tiles.