We present a propagation medium using a pair of non-identical coupled transmission lines (TLs). The slow wave characteristics of this coupled TLs are analyzed by generating fourth order dispersion relation as functions of (L, C) parameters. It it noted that higher order dispersion modes are generated by introducing coupling of two different modes on two different pairs of TLs. Depending on the choice of the coupling parameter (K) between these lines, upto fourth order dispersion can be achieved. A relation between geometry and higher order dispersion characteristics is presented. Slow wave characteristics are demonstrated using design example. Our analysis serves as a fundamental tool for the design of future novel geometries to achieve exotic dispersion modes for numerous microwave applications.