A nonlinear iterative scheme is developed to reduce the computing time of the Analytic Function Expansion Nodal (AFEN) method and is applied to three test problems, including a mixed-oxide fuel problem. The new nonlinear scheme is based on solving two-node problems and using two nonlinear correction factors at every interface instead of one factor, as in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents, which are used as the boundary conditions of the two-node problem. The numerical results show that this new nonlinear scheme reproduces the same solution as that of the original AFEN method and that the computing time is significantly reduced in comparison with the original AFEN method.