A covering of rectangular or square panels laid to form an assembly is disclosed, wherein the panels are arranged in a chequerboard pattern such that butt joints between the panels cross one another. Each panel has, at its border sides, grooves and tongues for horizontal locking and vertical locking with adjacent panels. The tongues for vertical locking are arranged on two adjacent border sides. The grooves for vertical locking are arranged on the other two adjacent border sides. One of the two tongues is fixed and the other tongue is movable. The panel to be laid first engages below the second panel to be laid subsequently for horizontal locking. For vertical locking, a locking edge is arranged on the first panel and a movable tongue, which can be displaced behind the locking edge, is arranged on the second panel, wherein each of the two tongues fits into each of the grooves for the vertical locking of such a panel.