According to the relation of the first surface integrality and the second surface integrality, the second surface integrality is translated to the first surface integrality via calculating the normal vectors of the surface. Simultaneously, the integrand is turned to the dot metrix of two vectors. By making use of the relation of the area element on the surface and the area element on the coordinate surface,the second surface integrality is straightly translated to the duplicate integrality under distinct conditions. Consequently, we are going to calculate the normal vectors on the surface and the duplicate integrality instead of the second surface integrality.