A negative insert for cutting machining has a top side, a clearance side perpendicular thereto and a cutting edge in a region interconnecting these sides and extending substantially in parallel with these sides. The insert has further a flat or rounded chamfer connecting the cutting edge to the clearance side on at least one lateral side of the insert in the region of a corner thereof. The chamfer makes an angle of 1°-15° with the clearance side for enabling application of the chamfer substantially tangentially to a work piece to be machined for bearing of the insert in two dimensions against the work piece during cutting machining operation carried out by the insert.