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 (50, 52) 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, 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, the coupling tongue extending between an abscissa z 1 and an abscissa z 3 along a longitudinal axis perpendicular to the longitudinal axis of the refill and to the pivot axis, the body extending between the abscissa z 1 and an abscissa z 2 along the longitudinal axis 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 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 (50, 52) 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, 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, - 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, the coupling tongue extending between an abscissa z 1 and an abscissa z 3 along a longitudinal axis perpendicular to the longitudinal axis of the refill and to the pivot axis, the body extending between the abscissa z 1 and an abscissa z 2 along the longitudinal axis 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 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.