Abstract: The invention relates to a highly accurate core bullet with a massive core (2) and a jacket (1) for a fire arm. The core (2) extends over the entire length of the bullet and has a diameter along at least the largest portion of its length which is significantly smaller than the outside diameter of the finished bullet (1). The invention also relates to a method for manufacturing such bullet by making a bullet blank (7) wherein the shank (4) and the most forward portion of the nose-end (3) are machined to finish size; by making the jacket blank (8) and attaching the same to the shank (4) of the core blank (7), wherein the jacket blank (8) has an oversized diameter and engages in a formfitting manner with the core blank (7) at a circular step (5) and, if necessary, at a shoulder at the rear head (6); and securing the bullet blank so made between turning centers and machining the final bullet contour with high precision centered with respect to the core.