A headlamp which contains a lamp is disclosed, with a headband enabling the lamp to be held on the head of a user is presented. The headband has a rigid/semi-rigid front section supporting the lamp using a pivot liaison. The pivot liaison allows rotation having: a first amplitude of at least 0 to +30 degrees and preferably 0 to 45 degrees to provide appropriate illumination when the lamp is worn in a conventional manner around the head. A second amplitude ranging from at least 0 to −45 degrees, and preferably 0 to −80 degrees provides appropriate illumination when the lamp is worn around the neck without being inverted. The 0 degree inclination corresponds to the pivot of the lamp which generates a horizontal light beam when the headlamp is positioned on the head of a standing user with the eyes fixing the horizon.