To provide a tightener that has a structure, for tightening a tapered hollow shaft 2 or the like having a slant face 8 or tightening extending slantingly inside a hollow shaft receiving space 7, wherein tightening jaws 6 provided on an operating spindle 5 are operable by an axially movable tightening head 3 guided in the operating spindle 5 and are pressed against the tightening slant face 8 via their slant faces 9 inclined in conformance with the tightening slant face 8, and that can advantageously shorten the time of the replacement of the tapered hollow shaft 2.

The operating spindle 5 has a holding clamp 10, which has holding tongues 11 extended parallel to the tightening jaws 6 and spring-loaded in a radial direction. The holding tongues 11 have holding faces 12 inclined in conformance with the tightening slant face 8. The holding faces 12 are pressed against the tightening slant face 8 when the holding tongues 11 are in a stopping/holding posture.