  Two different types of orthogonality condition models (OCM) are equivalently
formulated in the Faddeev formalism. One is the OCM which uses pairwise
orthogonality conditions for the relative motion of clusters, and the other is
the one which uses the orthogonalizing pseudo-potential method. By constructing
a redundancy-free T-matrix, one can exactly eliminate the redundant components
of the total wave function for the harmonic-oscillator Pauli-forbidden states,
without introducing any limiting procedure. As an example, a
three-alpha-particle model interacting via the deep alpha alpha potential by
Buck, Friedrich and Wheatley is investigated.
