In order to establish an optimum position on the upper side of the tibia for the exit point of an anterior cruciate ligament replacement, it is proposed that, with the leg bent, the position of a number of points along the front edge of the notch is detected and in this way their position and progression on the femur are also determined, that, with the leg straight, the course of this front edge of the notch is projected onto a projection plane which is perpendicular to the longitudinal axis of the tibia in the region of the upper side of the tibia, and that, within the region enclosed by this projected curve, the exit point is selected such that it maintains at least a distance corresponding to the radius of the implant from the projected curve. Furthermore, an apparatus for carrying out such a method is proposed.