A method which serves to display a new rectangular window in a display zone on a screen, the display zone already including at least one first rectangular window, the new window being displayed progressively towards the inside and starting from an edge of the first window is disclosed. In one aspect, the method comprises shifting the content of the first window from the edge through a distance corresponding to the dimension of said new window in a second direction perpendicular to a first direction parallel to the edge. The method may also comprise displaying the new window along the edge, the display having the effect of correspondingly reducing said first window in the second direction and, once the entire new window has been displayed, managing the scrolling of the initial content in the first window.