The extension of a relativistic double group configuration interaction (CI) formalism to the use of 2- and 4-spinors is presented. We first elucidate the theoretical aspects of the formalism that is needed to work with spinors that are optimized with a Hartree-Fock scheme that includes spin-orbit coupling. We then describe a new general implementation for the computation of sigma vectors and n-particle density matrices that occur in direct CI algorithms. Sample calculations of the spin-orbit splitting in atoms with one particle or hole in an otherwise closed shell configuration l(1) (l=1,2,3) and molecules containing such atoms illustrate the advantage of treating this effect in a basis of true spinors rather than in a basis of scalar relativistic orbitals as is conventionally done. (C) 2003 American Institute of Physics.