A self-centering metallic energy dissipating (SC-MED) structure usually consists of a total self-centering (TSC) system and metallic energy dissipating (MED) devices. Thus, the peak and residual displacement of SC-MED structures built in a seismic zone can be ameliorated. According to our previously proposed trilinear hysteresis model, we derived a nonlinear displacement ratio function (CR-R relation). This function can be used for the fast evaluation of the seismic displacement of an SC-MED system, with the assumption that the TSC system yields prior to the MED devices (this case is called “TSCY”). However, when a low-yield-point steel is employed as the MED material, the MED devices could yield earlier than the TSC system (this case is called “MEDY”). The hysteresis of TSCY and MEDY considerably varies. Owing to the various hysteresis behavior, MEDY can generally lead to less demand for both displacement and strength. Therefore, the CR spectra considering both TSCY and MEDY, and more possible parameter combinations, were investigated in this study. It was found that the effect of most of the key parameters on the CR spectra had the same trend as that in the previous study; however, some parameters had a contrary effect on TSCY and MEDY. On the basis of the result of a nonlinear history analysis and the statistical values of the renewed parameter combinations, we propose a revised CR-R relation here. On the basis of the data from two sets of earthquake records, this revised relation generally results in better prediction than that of the previous one, except when the value of αs is small for MEDY. Overall, the revised equations are conservative for practical design.