The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular approximation. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular approximation (IORA) rather than the zeroth-order regular approximation method. Further perturbational expansion of the exact relativistic electronic energy utilizing the effective Hamiltonian leads to new methods based on ordinary (IORAn) or double [IORAn(2)] perturbation theory (n: order of expansion), which provide improved energies in atomic calculations. Energies calculated with IORA4 and IORA3(2) are accurate up to c(-20). Furthermore, IORA is improved by using the IORA wave function to calculate the Rayleigh quotient, which, if minimized, leads to the exact relativistic energy. The outstanding performance of this new IORA method coined scaled IORA is documented in atomic and molecular calculations. (C) 2003 American Institute of Physics.