Abstract: An arrangement for holding a cutting tool is detachably fastened to a receiving member on the left or right side or turned 180.degree.. The arrangement includes a support and a clamp for firmly mounting at least one exchangeable cutting tip; for this purpose, in one embodiment, the support has a longitudinal groove and the clamp has a longitudinal serrated edge which extends into said groove.In order to hold the cutting tip even more exactly in place, the clamp has a serrated edge which engages in a shape-mating connection in a slot arranged on the rear face of the cutting tip.These tools are used especially as recessing tools on lathes.