Let the marine transmission using conical gears be called "Conical Drive Marine Transmissions". For these years, marine transmissions having high capacity have become an urgent need. To answer this need, it is necessary to increase both the tooth surface strength and the bending strength. The authors have already developed concave conical gears which made it possible to increase the tooth surface strength. And now, as the gears which makes it possible to increase the bending strength, we invented a new type of concave conical gear, called "Hyper Conical Gear". That is to say, the Hyper Conical Gear is the gear having both the increased tooth surface strength and the increased bending strength. This research aims at developing the design and production system of the Hyper Conical Gear. In this report, the first, the principle of generating method of the tooth surface is described, and the tooth surface is analyzed theoretically. Secondly, test gears are designed and made for trial. Finally, the tooth surface of the test gears are measured and compared with theoretical ones. And, it is proven that the generating method of"Hyper Conical Gear" has the availability. This research opens the way to conical drive marine transmissions having high capacity. In the 2nd report, the design and production method of a pair of these gears are reported.