Transmission-line models for electromagnetic transient simulation are usually based on the traveling-wave method. While recent developments have focused on phase-domain formulations with an emphasis on accuracy and passivity enforcement, no consideration has been given to ensure the symmetry of the model. In this paper, we introduce the symmetry preserving property (SPP) of the propagation matrix H as a way of enforcing a symmetrical model. This property is enforced by replacing the (unsymmetrical) propagation matrix H with the (symmetrical) propagated characteristic admittance matrix Y-p during the process of rational fitting. The propagation matrix H is recovered analytically for use in the final line model. We show a procedure for enforcement of SPP and the resulting model is implemented in an Electromagnetic Transients Program-like simulation environment. Although the computational efficiency decreases somewhat with the new approach, the symmetry of the model offers significant advantages. Besides being physically correct, it avoids confusion when performing sanity checking of complex network models.