The concept of contact is applied into the machining of the complex surface. If the contact line is along the straight line of cutter, the contact line should be along the asymptotic direction of the surface being machined. For the undeveloped ruled surface, the directions of the normal vectors are different, while the directions of the normal vectors on the straight line of cylinder are the same, so that there may be some over cutting on the surface. With the theory of this paper, the best cutter postural can be determined when the contact line is not along the straight line of the cutter. And further more, with the concept of third order contact, both the best cutter postural and contact direction can be determined at same time. This paper showed how to use this method for the machining of impeller leaf.