In this paper we present a new and improved formulation for the Multimode Equivalent Network (MEN) representation of arbitrary waveguide junctions. In the new formulation the Kummer's transformation is used to separate the kernel into dynamic and static parts, by introducing higher order extraction terms. The main difference with respect to the old formulation is that the approximation of the kernel is more accurate and the numerical computations are more efficient. In addition to theory, both formulations are compared in terms of efficiency and convergence thereby fully validating the proposed new formulation.