Abstract: When stokes integration is performed using the fast Hartley transform (FHT) techniques or fast Fourier transform (FFT) techniques,it must be modified as the explicit convolution form, then the convolution can be evaluated by FHT (or PFT) techniques. In this way,numerital quadature procedures which are usually time consuming can be avoided. However,Stokes formula itself does not strictly satisfy convolution definition so that its con-volution form includes an approximate term. Although such an approximation could meet some accuracy in most practical application, for higher accuracy application there still exist the inadmissible errors in the calculated results. This paper presents a method of spherical co-ordinate transformation which can effectively eliminate the errors due to the approximate term in the convolution form of stokes integration farmula.