Cosmetic refill intended to be inserted in a removable manner into a housing in a device for treating the hair, comprising - a body that has a first wall and a second wall opposite the first wall , - at least one coupling relief that extends from each of the first wall and the second wall , (i) the coupling relief on the first wall being intended to cooperate with a first surface of the housing when the first wall is introduced into the housing , (ii) the coupling relief on the second wall being intended to cooperate with a second surface of the housing when the refill is brought into a use position, by pivoting in the housing about a pivot axis (B), wherein the coupling relief on the second wall is an elastically deformable coupling tongue that has, on its surface facing the second surface , - at least one protruding relief to be inserted into a recessed relief in the second surface , or - at least one recessed relief for receiving a protruding relief on the second surface , the refill having an elongate shape along a longitudinal axis (X), the coupling tongue extending between an abscissa z 1 and an abscissa z 3 along a longitudinal axis (Z) perpendicular to the longitudinal axis (X) of the refill and to the pivot axis (B), the body extending between the abscissa z 1 and an abscissa z 2 along the longitudinal axis (Z) of the coupling tongue , the protruding relief(s) on or the recessed relief(s) in the coupling tongue extending between the abscissa z 1 and the abscissa z 2 along the longitudinal axis (Z) of the coupling tongue , wherein the distance |z 3 -z 1 | is greater than the distance |z 2 -z 1 | by a distance |z 3 -z 2 | greater than or equal to 1 mm. - a body that has a first wall and a second wall opposite the first wall , - at least one coupling relief that extends from each of the first wall and the second wall , (i) the coupling relief on the first wall being intended to cooperate with a first surface of the housing when the first wall is introduced into the housing , (ii) the coupling relief on the second wall being intended to cooperate with a second surface of the housing when the refill is brought into a use position, by pivoting in the housing about a pivot axis (B), wherein the coupling relief on the second wall is an elastically deformable coupling tongue that has, on its surface facing the second surface , (i) the coupling relief on the first wall being intended to cooperate with a first surface of the housing when the first wall is introduced into the housing , (ii) the coupling relief on the second wall being intended to cooperate with a second surface of the housing when the refill is brought into a use position, by pivoting in the housing about a pivot axis (B), - at least one protruding relief to be inserted into a recessed relief in the second surface , or - at least one recessed relief for receiving a protruding relief on the second surface , the refill having an elongate shape along a longitudinal axis (X), the coupling tongue extending between an abscissa z 1 and an abscissa z 3 along a longitudinal axis (Z) perpendicular to the longitudinal axis (X) of the refill and to the pivot axis (B), the body extending between the abscissa z 1 and an abscissa z 2 along the longitudinal axis (Z) of the coupling tongue , the protruding relief(s) on or the recessed relief(s) in the coupling tongue extending between the abscissa z 1 and the abscissa z 2 along the longitudinal axis (Z) of the coupling tongue , wherein the distance |z 3 -z 1 | is greater than the distance |z 2 -z 1 | by a distance |z 3 -z 2 | greater than or equal to 1 mm. <EOS>