PURPOSE: To provide a fitting tightening device which is capable of selectively turning a collet crimping machine at the horizontal position and in the vertical position, holding it at the selected position, and simple in structure and operation.

CONSTITUTION: A bracket 30 connected to a collet crimping machine 10 is turnably fitted to a pair of upstanding support arms 27, 28. A retainer to selectively retain the collet crimping machine at the desired turning position relative to a carrier 12 is provided. The retainer comprises a spring-urged detent pin 40 fitted to one of the support arms 27, 28. The detent pin is cooperated with a plurality of apertures formed piercing one part of the bracket to retain the bracket in one of a plurality of discrete positions defined by the apertures. The retainer is of the structure to retain the bracket arbitrarily in any one of an infinite number of positions relative to each support arm through the frictional gripping.