The analytic function expansion nodal (AFEN) method formulation for the solution to two-group diffusion equations in rectangular geometry is reformulated in the principle of the unified nodal method (UNM) formulation. Except for the corner point neutron balance equations, the nodal coupling relations of the reformulated AFEN method are shown to resemble exactly those of the nodal expansion method (NEM) so that they not only can be easily incorporated into the existing NEM production codes but also can enable one to make the most of the well-established numerical solution schemes including the nonlinear coarse-mesh finite difference (CMFD) schemes for speedy AFEN method calculations. A one-node CMFD scheme for the speedy AFEN calculations of the UNM formulation is newly proposed. The effectiveness of the one-node scheme is compared with that of the two-node CMFD scheme in terms of UNM solutions to the International Atomic Energy Agency and Organization for Economic Cooperation and Development L336 neutronics benchmark problems. Advantages of the UNM formulation for the AFEN method calculations over the original AFEN method formulation are discussed.