It is shown that, by using a unitarity relation for a many-body scattering amplitude, a Regge residue appearing in this amplitude is factorized. This theorem is a generalization of that in the t~o-body case. According to this theorem the famous level degeneracy in dual resonance models is expected to be removed, if unitarity is taken into account. We propose an eguation for removing the degeneracy, which has a close resemblance to that in the quantum mechanical perturbation theory with degenerate levels. shown that the number of resonant states with mass Sn, sn being defined by n =a (sn), is given by exp (aVn), (a= 2n/ -/6), for a large n. In other words, the N-point Veneziano formula has the extremely large number of degenerate levels. On the other hand, we can see in § 2 that, by using a unitarity relation for a many-body scattering amplitude, a Regge residue appearing in this amplitude is factorized, that is, the number of the states having mass sn is only one. This theorem is a generalization of that in the two-body case. 2 > The Veneziano amplitude violates unitarity in a way similar to that in which the Born approximation does in the usual Feynman-Dyson theory. It may be expected, therefore, that the level degeneracy in the dual resonance model will be removed if unitarity is taken into account. If, for the purpose of imposing unitarity, we sum up all the higher order diagrams in the framework of the operator formalism, the poles of the amplitude appear as poles of the propagator. Though the self-energy part of this clothed propagator is strongly divergent, we expect that some kind of renormalization procedure will be· possible. 3 > (We do not consider this procedure in this paper.) ln order to obtain the observed masses, that is, the zeros of the inverse propagator, we propose in § 3 a method very similar to that in the quantum mechanical perturbation theory with degenerate levels.