Headband for a headlamp which includes: a front part comprising a headband element configured to receive a lamp body , and comprising two terminations , wherein each termination comprises a passing hole or vertical conduit configured for the sliding passage of a tightening elastic link and a first attachment clip projecting to make a horizontal sliding connection with an electrically conductive cord , a rear part comprising a support intended to hold an electric battery and a locking lever , wherein the support of said rear part comprises at its base two attachment points - respectively left and right - for two ends of said tightening elastic link and further comprising two through holes in its upper part to ensure the passage of said tightening elastic link which can be blocked by said locking lever ; said tightening elastic link being configured to pass successively from said left attachment point on the base of the support of said rear part , to then run towards said vertical conduit of a first termination to come out of it and go to join the upper left through hole of said support to form therein an adjustable and lockable loop which can be locked by said locking lever , wherein said tightening elastic link comes out through the upper right through hole of said support, to join the vertical sliding conduit of a second termination and then join the right attachment on the base of the support;. an electrical conductor cord ; characterized in that the electrical conductor cord has two radii of curvature so as to form a "Z"; a first movable clip positioned at the first radius of curvature to ensure sliding of said electrically conductive cord with the upper part of said tightening elastic link ; a second movable clip positioned at the level of the second radius of curvature to allow said electrically conductive cord to slide with the lower part of said tightening elastic link . a front part comprising a headband element configured to receive a lamp body , and comprising two terminations , wherein each termination comprises a passing hole or vertical conduit configured for the sliding passage of a tightening elastic link and a first attachment clip projecting to make a horizontal sliding connection with an electrically conductive cord , a rear part comprising a support intended to hold an electric battery and a locking lever , wherein the support of said rear part comprises at its base two attachment points - respectively left and right - for two ends of said tightening elastic link and further comprising two through holes in its upper part to ensure the passage of said tightening elastic link which can be blocked by said locking lever ; said tightening elastic link being configured to pass successively from said left attachment point on the base of the support of said rear part , to then run towards said vertical conduit of a first termination to come out of it and go to join the upper left through hole of said support to form therein an adjustable and lockable loop which can be locked by said locking lever , wherein said tightening elastic link comes out through the upper right through hole of said support, to join the vertical sliding conduit of a second termination and then join the right attachment on the base of the support;. an electrical conductor cord ; characterized in that the electrical conductor cord has two radii of curvature so as to form a "Z"; a first movable clip positioned at the first radius of curvature to ensure sliding of said electrically conductive cord with the upper part of said tightening elastic link ; a second movable clip positioned at the level of the second radius of curvature to allow said electrically conductive cord to slide with the lower part of said tightening elastic link . <EOS>