A nonorthogonal localized basis-set implementation of the driven Liouville von Neumann (DLvN) approach is presented. The method is based on block-orthogonalization of the Hamiltonian and overlap matrix representations, yielding nonoverlapping blocks that correspond to the various system sections. An extended Hückel description of gold/benzene-dithiol/gold and gold/pyridine-dithiol/gold junctions is used to demonstrate the performance of the method. The presented generalization is an important milestone toward using the DLvN approach for performing accurate dynamic electronic transport calculations in realistic model systems, based on density functional theory packages that rely on atom-centered basis-set representations.