The invention relates to a bone-grinding instrument, in which the grinding head is joined, releasably via a coupling, to a driving part, wherein the grinding head is designed as a hollow cylinder with a rounded end face and is provided on the outer and/or inner wall with an abrasive coating having a particle size between 30 and 300 .mu.m, and to a hollow removal cylinder which is to be used together with this bone-grinding instrument. In place of an abrasive coating, this hollow removal cylinder has barbs, which penetrate into the bone core.