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 (Z11) 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 in a longitudinal direction, wherein the drive system comprises, to this end: - a longitudinal-displacement unit , which generates a first relative-displacement component (M15) between the receiving surface and the applicator roller in the longitudinal direction (L13), - a transverse-displacement unit , which generates a second relative-displacement component (M16) of the applicator roller with respect to the receiving surface , in a transverse direction (T13) that intersects the longitudinal direction (L13), and in the form of a back and forth movement that corresponds to a desired amplitude of the undulations , - and characterized by a yaw steering unit , synchronized with the longitudinal-displacement and transverse-displacement units , which steers and automatically adjusts, by means of a yaw motor , the yaw orientation (M22) of the central axis (Z11) of the applicator roller , considered in terms of azimuth about an axis known as the "yaw axis" (Z22) which is normal to a reference plane (P13) defined by the longitudinal direction (L13) and the transverse direction (T13), so as to confer on the reinforcing strip being laid a yaw orientation (M22) 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 (Z11) 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 in a longitudinal direction, - a longitudinal-displacement unit , which generates a first relative-displacement component (M15) between the receiving surface and the applicator roller in the longitudinal direction (L13), - a transverse-displacement unit , which generates a second relative-displacement component (M16) of the applicator roller with respect to the receiving surface , in a transverse direction (T13) that intersects the longitudinal direction (L13), and in the form of a back and forth movement that corresponds to a desired amplitude of the undulations , - and characterized by a yaw steering unit , synchronized with the longitudinal-displacement and transverse-displacement units , which steers and automatically adjusts, by means of a yaw motor , the yaw orientation (M22) of the central axis (Z11) of the applicator roller , considered in terms of azimuth about an axis known as the "yaw axis" (Z22) which is normal to a reference plane (P13) defined by the longitudinal direction (L13) and the transverse direction (T13), so as to confer on the reinforcing strip being laid a yaw orientation (M22) which corresponds to the yaw orientation of the laying trajectory to be realized. <EOS>