Abstract: An improved conformal mapping analysis is presented here for cases of a symmetric stripline filled with multilayered dielectric media with their interfaces parallel the ground planes or a medium having a relative dielectric constant which is continuously varying in a direction perpendicular to the ground planes. The transformed dielectric interfaces are determined directly by our new method, in which the speed of the required computation is believed to exceed that in the method given by K.V.S. Raoet al.1