Abstract: Glass sheets that have been raised beforehand to their softening point are moved along, progressively giving them a desired bent shape. Between an initial bending phase in which the sheets begin to adopt their shape and a final phase of bending, continuous blowing of air is performed, at a point along the line along which the sheets move, onto at least one face of the glass sheets, under conditions capable of asymmetrically influencing a final concavity of the bent glass sheets by comparison with a concavity that the final bending would have given without the blowing. The bending machine includes at least one nozzle blowing air continuously and arranged at a point on the line along which the sheets move after the sheets have begun to take shape and before the final phase of bending. The at least one nozzle is arranged to blow air asymmetrically onto the sheets.