The reduced frozen-core approximation (RFCA) that has been previously used for nonrelativistic calculations is extended to relativistic calculations. The RFCA adopts a new method for the orthogonalization of valence basis functions to core orbitals. Orthogonalization is performed using corelike basis functions consisting of fewer primitive basis functions than core orbitals. Dirac-Fock-Roothaan calculations on HI and ThO show that the relativistic RFCA can reduce computing time and closely reproduce the total and valence orbital energies and spectroscopic constants obtained by all-electron calculations.