  We propose a new type of three-cluster equation which uses two-cluster
resonating-group-method (RGM) kernels. In this equation, the orthogonality of
the total wave-function to two-cluster Pauli-forbidden states is essential to
eliminate redundant components admixed in the three-cluster systems. The
explicit energy-dependence inherent in the exchange RGM kernel is
self-consistently determined. For bound-state problems, this equation is
straightforwardly transformed to the Faddeev equation which uses a modified
singularity-free T-matrix constructed from the two-cluster RGM kernel. The
approximation of the present three-cluster formalism can be examined with more
complete calculation using the three-cluster RGM. As a simple example, we
discuss three di-neutron (3d') and 3 alpha systems in the harmonic-oscillator
variational calculation. The result of the Faddeev calculation is also
presented for the 3' system.
