This paper proposes a modified implementation of the Folded Line Equivalent transmission line model to represent three-phase transmission lines. The Folded line equivalent decomposes a line into its open circuit and short circuit contributions. We propose an alternative orthogonal matrix to transform single-phase transmission line parameters, voltages, and currents to the Folded Line Equivalent domain. Because the proposed matrix is orthogonal, it can directly represent bidirectional transformations using circuit components in simulation software, such as the ATP-EMTP. First, the circuit implementation of Clarke's matrix decouples a three-phase transmission line into its modes. Then, the circuit implementation of the proposed matrix decouples each mode into its open circuit and short circuit contributions. This paper proves that the proposed approach outputs similar results as those obtained by the Universal Line Model and the JMarti model in the simulation of transmission lines under open-circuit, energization, and fault conditions. However, because the proposed model does not derive from the method of characteristics, it can run with simulation times greater than the propagation delay of the transmission line. It is shown that the proposed approach outputs accurate results for time steps that are 10%, 100%, 200%, and 400% of the propagation delay of the transmission line. Thus, one major advantage of the proposed approach is that it can be used to reduce runtimes in the representation of short transmission lines in large complex networks by increasing time steps without compromising accuracy.