The present invention concerns the nose-piece of a laser-beam drilling head for a drilling machine, emitting a pulsed laser beam, where the drill head includes a resource which is suitable for mounting the nose-piece, where the nose-piece includes a first laser beam entry opening and a second pulsed laser beam exit opening and a beam focusing resource arranged upstream of the second opening, characterized by the fact that a mirror is positioned in the optical path of the laser beam downstream of the said beam-forming resource, so that the emerging beam forms an angle of less than 180° with the entering beam, and where the nose-piece includes a laser-beam fluid assisting feed that is arranged so that the said fluid is emitted via the second opening in the direction of the laser beam.