A clasp for a bracelet of the type comprising first and second free ends, the clasp comprising first and second fixing devices (14, 15, 26, 42, 48) of the bracelet which are intended to be fixedly joined to the first and second free ends of the bracelet, respectively, said fixing devices (14, 15, 26, 42, 48) being able to be moved relative to each other between at least one open configuration and one closed operational configuration in which they are closer to each other than in the open configuration in order to close the bracelet and to define an active length thereof, means (36, 38) for locking said bracelet fixing devices (14, 15, 26, 42, 48) in their closed configuration, the first bracelet fixing device comprising a frame which carries a device (42, 52, 58, 60, 76) for adjusting the active length of the bracelet comprising a carriage, which is intended to be fixedly joined to the first free end of the bracelet and which is capable of sliding inside said frame in the longitudinal direction of the bracelet, said carriage carrying a longitudinal locking member which is arranged so as to cooperate with an indexing member which is fixedly joined to said frame, in order to ensure that said carriage is retained in a predefined position relative to said frame, said longitudinal locking member being assembled with said carriage in such a manner that it can be moved, with reference thereto, between at least a first locking position, in which it cooperates with said indexing member, and a second adjustment position, in which it is out of range of said indexing member in order to enable a relative displacement between said carriage and said frame, characterized in that said carriage carries a resilient return member which is arranged so as to apply a force to said longitudinal locking member and to tend to position it in the locking position. first and second fixing devices (14, 15, 26, 42, 48) of the bracelet which are intended to be fixedly joined to the first and second free ends of the bracelet, respectively, said fixing devices (14, 15, 26, 42, 48) being able to be moved relative to each other between at least one open configuration and one closed operational configuration in which they are closer to each other than in the open configuration in order to close the bracelet and to define an active length thereof, means (36, 38) for locking said bracelet fixing devices (14, 15, 26, 42, 48) in their closed configuration, the first bracelet fixing device comprising a frame which carries a device (42, 52, 58, 60, 76) for adjusting the active length of the bracelet comprising a carriage, which is intended to be fixedly joined to the first free end of the bracelet and which is capable of sliding inside said frame in the longitudinal direction of the bracelet, said carriage carrying a longitudinal locking member which is arranged so as to cooperate with an indexing member which is fixedly joined to said frame, in order to ensure that said carriage is retained in a predefined position relative to said frame, said longitudinal locking member being assembled with said carriage in such a manner that it can be moved, with reference thereto, between at least a first locking position, in which it cooperates with said indexing member, and a second adjustment position, in which it is out of range of said indexing member in order to enable a relative displacement between said carriage and said frame, characterized in that said carriage carries a resilient return member which is arranged so as to apply a force to said longitudinal locking member and to tend to position it in the locking position.