A new table-direct CI (TDCI) scheme based on the table CI method for the direct computation of Hamiltonian matrix elements whose basis functions are linear combinations of spin-adapted functions psi(alpha) is presented, in which the explicit calculation and storage of the Hamiltonian matrix H in the basis {psi(alpha)} is avoided. Two algorithms are provided for the matrix element evaluation; (i) within the iterative Davidson diagonalization procedure of H and (ii) within the individualized configuration selection scheme of Buenker and Peyerimhoff, as included in the MRD-CI program of these authors. The new algorithm is employed to compute the equilibrium structural parameters of the lowest X (2)A(1) and A B-2(2) states of NO2, solving secular equations of dimension 190 000 spin-adapted functions (384 000 determinants, 32 000 configurations), as well as the T-e value for the corresponding transition.