Headlight for a motor vehicle comprising a reflector and a light source (S) running transversely to the optical axis (Y--Y) of the reflector and placed near the focal point of the reflector. The transverse light source (S) is placed near the internal focal point (Fi) of an ellipsoidal reflector (R1). The wall of the ellipsoidal reflector has a cutout (1) situated on one side of the plane passing through the geometric axis of the light source (S) and parallel to the optical axis (Y--Y) of the ellipsoidal reflector. A lens (2) with an optical axis parallel to or coincident with that of the ellipsoidal reflector (R1) is placed in front of this reflector, the focal point (3) of the lens being close to the external focal point (Fe) of the ellipsoidal reflector. A verticalized reflector (R2) is arranged on the opposite side of the cutout (1) to the most-part of the ellipsoidal reflector (R1), this verticalized reflector (R2) being designed to produce, from the source (S) housed in the ellipsoidal reflector, a long-range beam which is not intercepted by the lens, the ellipsoidal reflector giving a wide beam of shorter range.