We report the synthesis of a thin nematic elastomer film where the major director of the mesogenic moieties (i.e. the average orientation of the main molecular axes) is permanently oriented parallel to the film’s normal. This allows us to directly observe the orientation of the minor director (average orientation of the minor molecular axes) using optical techniques. We find that the elastomer exhibits spontaneous biaxiality at room temperature and the minor director is oriented in large domains. When a mechanical field is applied perpendicular to the major director, the domains of the minor director reorient into the direction of strain above a characteristic threshold, forming a monodomain with 3D orientational long-range order. This reorientation process is accompanied by a change in the slope of the stress–strain curve and X-ray scattering experiments reveal that the reorientation of the major director only sets in after the reorientation of the minor director is complete.