A method using an expansion of the components of the four-body Yakubovsky wave function in the basis of solutions to the Faddeev equation for the two-cluster sub-Hamiltonian eigenfunctions is proposed. This expansion reduces the Yakubovsky differential equations to a system of coupled-channel equations for functions depending on the relative coordinates of the subsystems of two-cluster partitions. On the basis of the resulting equations, the four-nucleon bound-state problem and the problem of zero-energy n³H scattering are solved with the aid of a relatively small computer.