The invention relates to a milling cutting insert having a square or triangular shaped cutting face delimited in the plan view by a peripheral cutting edge having linear cutting edges (10) and curved cutting corners (11). According to the invention, each of the cutting edges (10) comprises an inclined region (10a) sloping toward a cutting corner (11), extending beyond the tangential point (14) determined by the point at which the linear cutting edge (10) transitions into a curved cutting corner (11), wherein adjacent thereto the cutting edge (10b) rises prior to the point (24) determined by a cutting corner angle bisector (15), wherein said rising region (10b) extends to a cutting edge maximum (17) on the other side of the cutting corner (11) on the adjacent cutting edge (10), which is linear in plan view, from where the cutting edge (10) continues, again inclined and sloping downward, resulting in a rotationally symmetric form having identically shaped cutting edges.