To prevent the end of a paper sheet of or near the outermost layer contacting a binding band from being folded to be turned up in winding and binding with the binding band.

When the upper side of a bundle of bills swells in a longitudinal direction of the binding band to the end of the bundle along top presses 17 for pressing the upper surface of a large bundle A of bills in binding, as shown in Figs. (a) and (b), the ends of the bills on and near the topmost layer are easily turned up. A notch 174 is provided in the press 17 so that both ends of the notch 174 serve as first and second compression parts having a difference s in level. A deflection first generated toward the inside from the ends of sheets being pressed by the first compression part is held between by the second compression part contacted later for forming a protrusion in a direction crossing a binding band and for reducing the swelling in the longitudinal direction of the binding band.