The invention discloses a sheet processing machine with an alignment plate at the input. The sheets are piled against the plate, and during each machine cycle, the bottommost sheet is extracted and delivered to a gripper bar of the machine. The alignment plate can move precisely longitudinally and diagonally to adjust the position and the skew of the sheet for correct positioning in the gripper bar. The alignment plate is guaranteed to be kept vertical by using a pair of synchronized linear actuators on each side of the plate. The machine can adapt to varying sheet thickness by adjusting the gap below that plate thanks to a motorized gauge. To even better position the sheets, a set of abutments is provided after the plate, and at a fixed distance to the plate. The abutments are pivoting to get out of the way of the gripper bar when needed.