Bevel gears and hypoid gears are more complex transmission equipments. To avoid the change of shaft angles, the zero modification transmission (i.e.x₁ + x₂ = 0) tooth systems are adopted and had been used about one century .This paper introduces a new tooth system, NON-ZERO modification transmission (x₁+ x₂≠0), keeping the invariable shaft angle. After secondary development, this innovation may be manufactured by updated machine tool and be applied successfully to engineering vehicle, military production, vertical machine tool, locomotive, speed boat, as well as oil field, coal mine and cement industry. The new-type bevel gears have many advantages, such as multiple capacities, high reliabilities, long lives, small dimension, low noise and high adaptability. They not only may substitute the whole Gleason bevel gear system but also accomplish the function which Gleason can't. Hence the new type bevel gears will open vast vistas for application.