According to the invention, there is a new type of hole-provided indexable inserts, intended to be clamped in an insert holder by a clamp (11) that fixes the cutting insert both vertically and horizontally. The surface (29) of the cutting insert located around the centre hole (14) is an elevated or countersunk plane and has a star-shaped point shape having at least 6 points, adapted to constitutecontact surfaces for the lower, pairwise-arranged part surfaces of the clamp upon the tightening of the tightening screw (21).