A new method to cut the spiral bevel gears of Klingelnberg cyclopalloid system is proposed. The feature of the cutter used in this method is the straight cutting edge whose extension line does not pass through the cutter axis. The blade having a cutting edge can be made easily and its rake face can be reground to sharpen the cutting edge with an ordinary surface grinding machine. In the method, the pinion is generated with a complementary crown gear and the gear is generated with a newly introduced Pseudo-complementary crown gear. The pseudo-complementary crown gear is the generating gear whose pitch plane is not tangent to the pitch cone of work gear. The tooth (tool) surface of each crown gear is made up with the above mentioned cutter. The availability of the method is confirmed by trial gear manufacturing.