A generalized linear scaling localized-density-matrix (LDM) method is developed to adopt the nonorthonormal basis set and retain full Coulomb differential overlap integrals. To examine its validity, the method is employed to evaluate the absorption spectra of polyacetylene oligomers containing up to 500 carbon atoms. The semiempirical Hamiltonian for the pi electrons includes explicitly the overlap integrals among the pi orbitals, and is determined from the ab initio Hartree-Fock reduced single-electron density matrix. Implementation of the generalized LDM method at the ab initio molecular orbital calculation level is discussed.