Abstract: Two vertically displaceable slides (5, 9) carry in horizontally movable fashion a tabletop (1) and, respectively, a gripper with an upper gripper jaw (6) and a gripper base (7). The gripper base (7) contains a horizontally displaceable blade (12) and supporting elements (24, 25) which are horizontally displaceable and also vertically movable with respect to the blade (12). A Stack of sheets is set up in front of the tabletop (1). The slides (5, 9) are lowered until the upper gripper jaw (6) rests on the sheet stack. The blade (12), previously retracted into the gripper base (7), is then made to pierce the stack of sheets at an exactly settable distance below the upper gripper jaw (6). The slides (5, 9) are slightly elevated in order to form a gap in the sheet stack with the blade (12). The supporting elements (24, 25) are pushed into the gap below the blade (12), and are then urged upwardly past the level of the blade (12) so that they alone bear the weight of the sheets resting thereon.