Abstract: Sheet materials in the form of remnants of non-repetitive shapes and that might be flawed, e.g. hides (10), are cut up using a method that includes the following operations: digitizing the geometrical shape of each remnant; defining a layout for pieces to be cut out from the remnant; and cutting out the pieces from the remnant in compliance with the resulting layout. The surface of the remnant (10) is provided with marks characteristic at least of the disposition and of the orientation of the remnant during digitization. The marks are detected so as to generate and record position information representative of the positions of the first marks.