The cutting tool assembly of the present invention consists essentially in (a) a tool holder and (b) an indexible cutting insert of modified rhombic configuration in which pairs of main cutting edges (disposed at an angle of less than 60* with respect to each) are separated by intermediate facing edge portions which are parallel to each other. The intermediate facing edge portions are so configured as to constitute outfacing cutting edges each of which cooperates with the main cutting edge adjacent thereto. Both the pairs of main cutting edges and the out-facing cutting edges are provided with chip-breaking grooves. The assembly provides an arrangement wherein not only the main cutting edge but also the out-facing cutting edge of the cutting insert are laid bare with respect to the tool holder.