A cutting insert for turning includes a polygonal body of a hard, wear-resistant material, which has an upper surface and a lower surface, and a plurality of edge surfaces uniting the surfaces. At least one rounded cutting corner, provided with a nose-cutting edge, is formed at a nose portion at the area of the intersection area of two edge surfaces. The cutting corner defines a bisector. At least one recess is arranged in a support surface of the upper surface at a distance from the nose-cutting edge. The recess has a general extension toward the nose portion. Each recess is elongate and has successively increasing depth toward the nose portion.