The machine is comprised of a cabinet wherein besides units for collecting, stretching and conveying the sheets, there is mainly provided a cylinder (1) whereover each sheet (9) is pulled by tongs (12,13) moving along the lengthwise direction over said cylinder (1), characterized in that said cylinder is comprised of a torsion tube (1), and means are provided to twist said torsion tube (1) with motors (7,8) acting on the tube ends, about the lengthwise axis thereof as a function of the sensed faulty position of the sheet edge relative to the lengthwise axis of said torsion tube (1).