Abstract: An offset printing press is provided, including at least one unit for printing a web of paper, a device for transversely cutting the web of paper arranged downstream of the printing unit, and at least one system for controlling the printing unit. The control system is suitable for controlling, when the web of paper is moving, the implementation of steps involving: a) moving the printing unit into a throw-off configuration, the web of paper moving in the space delimited between the blanket cylinders, b) slowing down or accelerating the plate cylinder in order to modify the adjustment of the cutting register between the printing unit and the cutting device, c) moving the printing unit into a throw-on configuration.