A display device which is connected, in data terms, to a printing press, is controlled. A depiction of a printed image, which is printed onto a printing material by the printing press, together with a plurality of ink zones, arranged next to one another transversely, with respect to a transport direction of the printing material which is guiding through the printing press, of at least one inking unit, which is arranged in the printing press, are indicated on a display surface of the display device of a control unit in a controlled manner. The inking zones are indicated by way of parallel boundary lines, which delimit them in each case. For the display of the boundary lines which delimit the inking zones, the control unit fixes one of the color thereof and the brightness thereof and the opaqueness thereof in a manner which is dependent on a minimum contrast which has previously been set in the control unit, in order to form an image region, adjoining the boundary lines, of the printed image which is displayed on the image surface of the display device and displays the boundary lines which delimit the inking zones in the contrast ratio which is fixed in respect of the printed image which is displayed on the display surface of the display device.