Abstract: Using a novel approach, the analytic expressions of the A parameters (ABCD-parameters)for the asymmetric coupled transmission lines in inhomogeneous medium (ACTLIM) are derived in this paper . The expressions of the A parameters for the ACTLIM expressed by normal mode parameters are given. Which are explicit in expression and clear in the conception. Using the matrix operations, the presented expressions have been approved by results derived from the Z matrix. It is also showed that the novel method presented in the paper is very effective. Using the derived A parameters, the bandstop filter composed of the cascade of two open circuited sections of the asymmetric supported broadside-coupled coplanar waveguide is designed. The A parameters of the ACTLIM given in the paper will provide powerful theoretical tool for the application of the ACTLIM in the three dimensional (multilayer) microwave integrated circuits.