A luminaire has a concave reflector with an optical center on an optical main axis in an optical main plane. A screen extends along the optical main axis to a light emission window. The reflector has a first faceted reflector portion at a first side of the optical main plane, the optical center being its focus and the optical main axis being its axis. A second faceted reflector portion is present at a second side of the optical main plane, having a secondary axis passing through and a focus lying in the optical center. The secondary axis is tilted with respect to the main axis through acute angles in the main plane as well as out of the plane. The luminaire produces a screened-off light beam which is horizontally and vertically asymmetrical, which makes the luminaire suitable for an illumination of highways in a counter-traffic direction.