A device for attaching an object on a rail of a support is provided. The device includes a base designed to bear on the rail, and a device for tightening the base on the rail. The tightening device includes a threaded rod and a nut. A first end of the tightening device includes a tightening heel designed to be placed below the rail to tighten the rail between the heel and the base. A second end of the tightening device includes an element for maneuvering by an operator to tighten/loosen the device. The device can further include a detachable non-return device to prevent any involuntary loosening of the device.