A cutting insert holder (104) for releasably clamping a quadrilateral cutting insert (110) in a predetermined clamping position, the cutting insert (110) having a through bore (164) and a non-obtuse insert mounting corner. The cutting insert holder (104) includes a a clamping portion (116) formed with a wedge supporting surface (118) and a locking pin (116) received in the through bore (164). A clamping wedge (134) abuts the wedge supporting surface (118) and has an insert receiving pocket (180) with a pair of pocket side walls (184, 186) meeting at an insert receiving corner (188) for receiving the insert mounting corner (124). In a top view of the base surface a normal to the wedge supporting surface (118) passing through a center of the locking pin (166) passes through a first pocket side wall of the pair of pocket side walls (184, 186).