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The finite range expansion method [Y. Koike, Prog. Theor. Phys. 87 (1992), 775], which gives well converged solutions of the three-body Faddeev equations, is extended to the three-body and two-two subsystems in order to solve the four-body Faddeev-Yakubovsky equations. A feasibility study is carried out to check the convergence in a four-nucleon system at 3.45 MeV below the four-body break-up threshold, which is in between the 2N-2N and 2N-N-N break-up thresholds. We obtain a converged phase shift and inelasticity parameter to 6 digits for 3N+N elastic scattering.