Previous papers in this series have dealt with those types of electrochemical problems where discretization of the partial-difference equations automatically led to tridiagonally structured equations when using a matrix notation. It was shown that tridiagonal matrix equations can be solved very efficiently so that the full power of the implicit finite-difference methods can be exploited for a large class of electrochemical problems. In principle, any electrochemical mechanism composed of charge transfer steps and first- and second-order chemical reactions can be simulated in this way, and even the inclusion of IR-drop or adsorption phenomena does not significantly affect the speed of these simulations. However, there is another class of electrochemical problems for which the discretized implicit equations cannot be expressed directly in terms of tridigonal matrix equations and the fast implicit finite-difference, (FIFD) approach no longer seems to be applicable. A generalization of the FIFD approach which overcomes this drawback, so that the efficiency of this method becomes amenable to virtually any class of electrochemical problems, is presented in this paper.