PURPOSE: To enable a plane to be machined to be cut in a form closely resembling a straight line by utilizing a cutting tip with its cutting edge formed in a convex shape, in a throw-away type angular cutting employed for stainless steel chamfering work and the like.

CONSTITUTION: The cutting edge 5a of a cutting tip 5 is formed in a convex shape, and mounted with a screw 6 on the cutting-tip mounting flute 4 adjacent to a chip pocket 3 positioned on the peripheral portion of a conical cutter body 1. This cutting edge 5a is formed by a rake plane close to the chip pocket 3 and a flank on the peripheral surface, and a plurality of the cutting edges are arranged aslant on the peripheral portion of the conical cutter body 1 so that the mounting centers of the cutting tips 5 are arranged in the arc-form as a whole. A negative rake angle α is given in the radial direction of the cutting face, and this is dependent on the corner angle α and the axial rake angle β of the cutter body 1. The angle β is selected between 30° and 60°. With this cutter, the plane to be machined is cut in the form closely resembling a straight line, since the rotary locus of the cutting edge 5 agrees roughly with the cutting face form.