PPP MO theory initiated in 1953 a reliable SCF approach to excited states in multielectronic systems. Further developments, such as Del Bene-Jaffk's c m / s method, modified Pople's c m all-valence electron (AVE) approach to improve the results but maintained some basic troubles of this theory which were not in the PPP method. A new approach to SCF-MO-NDO calculations with a priori chosen parameters and configuration interaction of singly excited states is developed in this paper from the ground considerations of the PPP method and it is called CNWL. Thus, AVE m approximations have been modified in order to take into account independent monocentric terms in the Fock matrix elements for each kind of azimuthal quantum number atomic orbitals in the basis set. The only input data are Slater exponents, valence state ionization potentials, and electron affinities of each kind of atomic orbital. No parameters are empirically adjusted to fit results to experimental or previous accurate theoretical data. CNDOL is suitable for obtaining theoretically consistent results in polyatomic systems which are too large to be treated by more sophisticated procedures. Applications to hydrocarbons are shown which compare PPP results with the new AVE approach derived from it here.