An efficient procedure is presented to determine the implicit exact solution of an arbitrary nonuniform transmission line (NTL), and its first order approximation (F. O. A. ) as an explicit expression. The method of the solution is based on the steplines approximation of the nonuniform transmission lines and quasi-TEM assumptions. Using steplines approximation the NTL is subdivided into a large number of uniform line segments (steps). Using time-domain approach and invoking the boundary conditions at the discontinuities of the adjacent steps, each step is modeled as continuous time domain linear filter characterized by a transfer function. The frequency domain transfer function of this filter is then obtained for linear termination networks. For very large number of steplines this transfer function approaches transfer function of the NTL. In the next step a F. O. A. , as an explicit expression of the exact response will be obtained. This F. O. A. is more suitable for very short transmission lines which is often the case in integrated circuits and some of printed circuit boards. Then, the F. O. A. of the ABCD matrix will be obtained.