The acetabular cup bur comprises four blades (1, 2, 3, 4) which are preferably stamped out of non-hard metal sheets, e.g. stainless steel. The blades have slits (6, 7, 8, 9, 10) which enable them to be inserted into each other in order to obtain a bur head. The slits have different widths, enabling more than two of them to be assembled on the axis of rotation. Each blade is extended by a lower part (19). Said lower parts are driven by a flat ring (15) which keeps them rigid. The blades are stamped. The cutting wire (18) of the blade is obtained by the same stamping operation due to an appropriate form of the stamps.