Abstract: Apparatus for the fast angular orientation of a surgical instrument with respect to an implantation seat of a prosthesis in a patient's bone, of the type comprising a moving sensor, which may be associated with the surgical instrument, and a fixes sensor, which may be integrally fastened to the bone during a surgical operation, the moving sensor and the fixed sensor being provided with a position detection device and with a device for signaling of the detected position to a central memory and processing unit. The central memory and processing unit comprises calibration device which detect the position of the moving sensor when it is associated with a line passing through two known points of the bone and, simultaneously, they detect the position of the fixed sensor when it is integrally fastened to the bone, and they record such position as initial work position.