Abstract: A flooring system combines a dimensionally stabilized sub-floor laminate with a dimensionally stabilized tile laminate, the sub-floor laminate and the tile laminate being held together by magnetic attraction. In one embodiment one or other of the laminates is magnetic, and the other has a ferromagnetic engagement sheet. In another embodiment, a magnetic intermediate sheet is placed between ferromagnetic strata of the two laminates. The tile laminate may include ceramic tiles, which may be glass or porcelain. Those tiles are substantially rigid. They have flat ground edges to provide abutting matching fit with adjacent tiles. On assembly, neither mortar nor grouting is employed. The sub-floor has pre-defined mounting hardware accommodations that permit the fasteners not to interfere with the flatness and fit-up of the laminates.