A machine for processing a sheet of printing material contains a first chain conveyor having a first gripper bar for holding a leading edge of the sheet, and a second chain conveyor having a rear gripper bar for simultaneously holding a trailing end of the sheet. A processing device is assigned to the chain conveyors for processing the sheet. A distance changing device is provided for temporarily reducing a gripper distance between the two gripper bars and, consequently, producing a sheet sag required for the processing of the sheet carried out by the processing device. The distance changing device defines a first circulation path of the front gripper bar, determined by the first chain conveyor, and a second circulation path of the rear gripper bar, determined by the second chain conveyor, running locally differently from each other. The processing device can be, for example, a sheet smoother.