A method for displaying an outside scene on a cockpit display system. The system comprises two display areas contiguous along a horizontal aircraft axis and a processor to generate the display, on one of the areas, of an initial scene image from data from the aircraft's avionics electronics, the data comprising the aircraft's sideslip angle β. The processor displays, on the scene image, a flight path vector indicating a point on the scene image towards which the aircraft is heading. When the measured angle β exceeds a threshold, the processor displays the initial scene image on a first display area and the display of a supplementary outside scene image, on a second display area, the supplementary scene image representing a lateral extension of the initial scene image. The processor also displays the flight path vector superimposed on one of the two images based on a value of angle β.