The present invention relates to a headlight system (2) for a vehicle for making available a cornering light function. The headlight system (2) comprises a first light module (3) for generating a conventional asymmetrical dipped headlight which has an upper first light/dark boundary (25) on the driver's side A of a central axis V which is oriented so as to be horizontal. The headlight system (2) also comprises a second light module (4) which comprises a plurality of light-emitting diode units (13) which are arranged in the manner of a matrix, a control unit (16) which is coupled to at least the second light module (4) and is designed to actuate the light emissions of the individual light-emitting diode units (13) of the second light module (4) separately, and a bend-detection unit (19) with which the radius of a bend in the direction of travel of the vehicle (1) can be detected. The headlight system according to the invention is characterized in that the light-emitting diode units (13), which are arranged in the manner of a matrix, of the second light module (4) have at maximum two horizontal lines (12-1, 12-2), and by means of the light emissions of the light-emitting diode units (13) it is possible to generate an emission characteristic with a lower second light/dark boundary (30) which is below the first light/dark boundary (25) of the dipped headlight, an upper third light/dark boundary (29) which is above the first light/dark boundary (25) of the dipped headlight, and a lateral fourth light/dark boundary (31) on the side of the light emissions (28) of the second light module (4) which faces the driver's side and in order to make available a cornering light function, the control unit (16), the bend-detection units (19) and the second light module (4) are embodied in such a way that a cornering light angle (δ) which the outermost of the light beams which generates the lateral fourth light/dark boundary (31) encloses with the vehicle longitudinal axis L in the horizontal direction can be varied, and that this cornering light angle (δ) depends on the radius of the bend detected by the bend-detection unit. The invention further relates to a corresponding method for making available a cornering light function.