A tile system, comprising: —a mounting unit, e.g. a rail fixed to a wall; —a tile unit, e.g. a frame holding a decorative tile; —a tile unit-fastening device configured to fasten the tile unit to the mounting unit, e.g. a pin engaging recesses formed on the mounting and the tile unit, the tile unit-fastening device preferably comprising a repositioning mechanism configured to allow the tile unit to move in one or two directions parallel to the wall after the tile unit is fastened to the mounting unit, e.g. the pin having ribs on its outer surface and the recesses being elongated and having cooperating ribs on their elongated inner faces.