Performance-based earthquake engineering (PBEE) concepts dictate that the return period of the seismic design ground motions be known. While the NEHRP (2001) seismic design spectrum is constructed using two spectral accelerations that have a 2,475-year return period, the overall spectral shape is not representative of a uniform hazard spectrum. Consequently, other than the two spectral accelerations used to construct the NEHRP spectrum, the return periods of the spectral accelerations defined by the NEHRP spectrum are unknown and may vary significantly. An alternative spectrum is proposed for firm rock sites. The proposed parabolic spectrum is constructed using three spectral accelerations (i.e., pga, SS, and S1) and a calibration parameter Tpga. Parabolic spectra were computed for approximately 500 cities across the conterminous 48 states using the pga, SS, and S1 having 2,475-year return period, as determined by the U.S. Geological Survey National Seismic Hazard Mapping Project. The correlation coefficients (r2) of the parabolic spectra to spectral accelerations for several oscillator periods having uniform probabilities of exceedance were computed for the cities. The results confirm that the spectral accelerations defined by the parabolic spectra have approximately constant return periods.