Grinding machine with a machine bed, with a tool carriage that is linearly movable on the machine bed in a Y-axis, with a tool spindle, which is mounted in the tool carriage so as to rotate around an X-axis that is perpendicular to the Y-axis, and which can be rotationally driven, with an X-carriage that is linearly movable on the machine bed in the X-axis, with a Z-carriage that is linearly movable on the X-carriage with a Z-axis that is perpendicular to the X-axis and the Y-axis, and with a work piece jig, which is arranged on the Z-carriage so as to pivot around a B-axis, which is parallel to the Y-axis, and which is capable of rotating around its A-axis, which is perpendicular to the B-axis.