Abstract: To enable the position and orientation of an instrument which machines a bone to be determined relative to the bone without the need for X-radiation, the invention proposes a method for representing an instrument relative to a bone, in which the structure of the bone in a working plane passing through the bone is determined by means of an ultrasound head which emits and receives ultrasonic radiation in the working plane, in which the three-dimensional position and orientation of the bone and of the ultrasound head are determined by navigation, and from this information the position and orientation of the structure of the bone in a system of coordinates that is fixed with respect to the bone is determined, in which the ultrasound image in this working plane is represented on a display, in which the navigated instrument is aligned in such a way relative to the bone that its working direction is located in the working plane, and in which the working region of the instrument in the working plane is copied in the