This invention relates to a method for adhering floor tiles together and the flooring system thereby created. The method utilizes individual adhesive units as fasteners for attachment of each floor tile to the next contiguous floor tile. The adhesive units are a multi-layered composite comprised of at least one adhesive layer and at least one layer of polymer film or textile substrate. When a series of floor tiles are attached to one another in this manner, a floating floorcovering article is achieved.