An arrangement comprising a rail and a rail clamp, the rail, elongated along a first longitudinal axis, having a web extending between a head and a foot, the clamp comprising: - a frame disposed on the rail so as to be elongated along said first longitudinal axis and on which are successively mounted, along the first axis: - at least one device for hooking the rail able to occupy an engaged state under the rail along a second axis transverse to the first axis, said at least one hooking device being adapted, in the engaged state, to hook the rail at the web, just under the head, and - at least one actuator adapted to act on the rail in order to apply a force thereto oriented along a third axis transverse to said first and second axes (11, 12), and - a control unit capable of controlling said at least one actuator so as to apply to the rail, in a plane parallel to said first and third axes (11, 13), a righting torque, between the acting actuator and the engaged hooking device, characterised in that: - said at least one hooking device is mounted tilting relative to the frame around the second axis, and/or, - said at least one hooking device comprises: - a pair of jaws adapted so that, in the engaged state, the jaws hook the rail, on either side of the rail, along the second axis, and - several said actuators and wherein the jaws of said pair of jaws are mounted to move in translation on the frame along the second axis and are controlled by the control unit able to coordinate the mobility of the pairs of jaws and the actuators. - a frame disposed on the rail so as to be elongated along said first longitudinal axis and on which are successively mounted, along the first axis: - at least one device for hooking the rail able to occupy an engaged state under the rail along a second axis transverse to the first axis, said at least one hooking device being adapted, in the engaged state, to hook the rail at the web, just under the head, and - at least one actuator adapted to act on the rail in order to apply a force thereto oriented along a third axis transverse to said first and second axes (11, 12), and - a control unit capable of controlling said at least one actuator so as to apply to the rail, in a plane parallel to said first and third axes (11, 13), a righting torque, between the acting actuator and the engaged hooking device, characterised in that: - said at least one hooking device is mounted tilting relative to the frame around the second axis, and/or, - said at least one hooking device comprises: - a pair of jaws adapted so that, in the engaged state, the jaws hook the rail, on either side of the rail, along the second axis, and - several said actuators and wherein the jaws of said pair of jaws are mounted to move in translation on the frame along the second axis and are controlled by the control unit able to coordinate the mobility of the pairs of jaws and the actuators. - said at least one hooking device is mounted tilting relative to the frame around the second axis, and/or, - said at least one hooking device comprises: - a pair of jaws adapted so that, in the engaged state, the jaws hook the rail, on either side of the rail, along the second axis, and - several said actuators and wherein the jaws of said pair of jaws are mounted to move in translation on the frame along the second axis and are controlled by the control unit able to coordinate the mobility of the pairs of jaws and the actuators.