The present invention relates to an instrument for tensioning a flexible tie (14) used for fastening an implant on a bony element of a patient by forming a first loop around the bony element. Said instrument comprises: a rod (42) having a first end provided with bearing means (44) for bearing against said implant; a moving part (46) that is movable in translation and that surrounds said rod (42) over a fraction of its length, said moving part including holder means (50) for holding the end of said tie; and control means (52) mounted on said moving part (46) to cause the moving part to move relative to said rod, thereby tending to move the first end (42a) of the rod away from said moving part, thereby exerting tension on said tie relative to said implant.