Clasp with an extensible buckle for a bracelet enabling the length of the bracelet to be adjusted, said clasp comprising: - a central support, - a first and second pivoting strip (2a, 2b) articulated at either end of the central support and capable of being closed on the latter, - means for opening and closing (14, 16, 17, 19, 22) the clasp arranged in such a way as to lock the first and second pivoting strip (2a, 2b) against the central support and to unlock said first and second pivoting strip (2a, 2b) from the central support so they can be extended, - at least one of a first attachment solid with the first pivoting strip and arranged so as to be connected to a first strand of the bracelet and a second attachment solid with the second pivoting strip, and arranged so as to be connected to a second strand of the bracelet; the clasp furthermore comprises an attachment body arranged on at least one of the first and second pivoting strips (2a, 2b), the attachment or each first and second attachment (6a, 6b) being connected to the corresponding attachment body, which latter is capable of being displaced in the longitudinal direction of the corresponding pivoting strip (2a, 2b) to be locked in various positions along said strip (2a, 2b) characterised in that the pivoting strip or each pivoting strip (2a, 2b) comprises a bolt arranged to operate in conjunction with the corresponding attachment body, the bolt being capable of assuming respectively a first and a second axial position so that the attachment body or each attachment body can be locked in one of the various indexed positions when the bolt is situated in one of the first and second axial positions, and in such a way that the attachment or each attachment body can be unlocked in order to be able to slide inside the corresponding hollow to assume another indexed position when the bolt is situated in the other of the first and second axial positions, the bolt is arranged to cross the longitudinal edges (2, 2') of the pivoting strip or each pivoting strip (2a, 2b) as well as the attachment body along a perpendicular axis in the direction of displacement of the said body. - a central support, - a first and second pivoting strip (2a, 2b) articulated at either end of the central support and capable of being closed on the latter, - means for opening and closing (14, 16, 17, 19, 22) the clasp arranged in such a way as to lock the first and second pivoting strip (2a, 2b) against the central support and to unlock said first and second pivoting strip (2a, 2b) from the central support so they can be extended, - at least one of a first attachment solid with the first pivoting strip and arranged so as to be connected to a first strand of the bracelet and a second attachment solid with the second pivoting strip, and arranged so as to be connected to a second strand of the bracelet; the clasp furthermore comprises an attachment body arranged on at least one of the first and second pivoting strips (2a, 2b), the attachment or each first and second attachment (6a, 6b) being connected to the corresponding attachment body, which latter is capable of being displaced in the longitudinal direction of the corresponding pivoting strip (2a, 2b) to be locked in various positions along said strip (2a, 2b) characterised in that the pivoting strip or each pivoting strip (2a, 2b) comprises a bolt arranged to operate in conjunction with the corresponding attachment body, the bolt being capable of assuming respectively a first and a second axial position so that the attachment body or each attachment body can be locked in one of the various indexed positions when the bolt is situated in one of the first and second axial positions, and in such a way that the attachment or each attachment body can be unlocked in order to be able to slide inside the corresponding hollow to assume another indexed position when the bolt is situated in the other of the first and second axial positions, the bolt is arranged to cross the longitudinal edges (2, 2') of the pivoting strip or each pivoting strip (2a, 2b) as well as the attachment body along a perpendicular axis in the direction of displacement of the said body.