Device for laying a reinforcing strip for reinforcing a tyre, preferably a pneumatic tyre, said device comprising: - a receiving surface, - a laying head bearing an applicator roller which is mounted in a rotatable manner on a central roller axis so as to be able to feed a reinforcing strip by rolling and to press said reinforcing strip against the receiving surface, - a drive system for creating a relative movement of the laying head with respect to the receiving surface so as to be able to make the reinforcing strip laid on said receiving surface follow a path referred to as the "laying trajectory" which has a succession of undulations (14A, 14B, 14C) in a longitudinal direction, wherein the drive system comprises, to this end: - a longitudinal-displacement unit, which generates a first relative-displacement component between the receiving surface and the applicator roller in the longitudinal direction, - a transverse-displacement unit, which generates a second relative-displacement component of the applicator roller with respect to the receiving surface, in a transverse direction that intersects the longitudinal direction, and in the form of a back and forth movement that corresponds to a desired amplitude of the undulations (14A, 14B, 14C), - and characterized by a yaw steering unit, synchronized with the longitudinal-displacement and transverse-displacement units (15, 16), which steers and automatically adjusts, by means of a yaw motor, the yaw orientation of the central axis of the applicator roller, considered in terms of azimuth about an axis known as the "yaw axis" which is normal to a reference plane defined by the longitudinal direction and the transverse direction, so as to confer on the reinforcing strip being laid a yaw orientation which corresponds to the yaw orientation of the laying trajectory to be realized. - a receiving surface, - a laying head bearing an applicator roller which is mounted in a rotatable manner on a central roller axis so as to be able to feed a reinforcing strip by rolling and to press said reinforcing strip against the receiving surface, - a drive system for creating a relative movement of the laying head with respect to the receiving surface so as to be able to make the reinforcing strip laid on said receiving surface follow a path referred to as the "laying trajectory" which has a succession of undulations (14A, 14B, 14C) in a longitudinal direction, - a longitudinal-displacement unit, which generates a first relative-displacement component between the receiving surface and the applicator roller in the longitudinal direction, - a transverse-displacement unit, which generates a second relative-displacement component of the applicator roller with respect to the receiving surface, in a transverse direction that intersects the longitudinal direction, and in the form of a back and forth movement that corresponds to a desired amplitude of the undulations (14A, 14B, 14C), - and characterized by a yaw steering unit, synchronized with the longitudinal-displacement and transverse-displacement units (15, 16), which steers and automatically adjusts, by means of a yaw motor, the yaw orientation of the central axis of the applicator roller, considered in terms of azimuth about an axis known as the "yaw axis" which is normal to a reference plane defined by the longitudinal direction and the transverse direction, so as to confer on the reinforcing strip being laid a yaw orientation which corresponds to the yaw orientation of the laying trajectory to be realized.