An aircraft has a vertical fin fastened to the rear and above a fuselage of elongated form, essentially in a vertical plane of symmetry of the aircraft. The vertical fin has at least two stable positions, an extended position and a returned position, such that a surface of the vertical fin, subjected to an aerodynamic flow when the aircraft is in flight, is modified in position or in surface between the returned position and the extended position, so that the aerodynamic drag of the vertical fin is reduced in the returned position under given flight conditions compared to the extended position. The change from one surface to another of the vertical fin is accomplished by modifying the geometry of the vertical fin or by displacing the vertical fin relative to the fuselage so that the vertical fin, for example, is more or less inside the fuselage, or more or less immersed in the wake zone of the fuselage in which the local dynamic pressure Pd is reduced relative to the infinitely upstream dynamic pressure Pd0.