The duality property of hadron scattering amplitudes has been now recognized as fundamental, but its concrete representation has not been established yet. The finite-energy sum rule is not symmetric in treating two dual channels. The Veneziano-type models have, at present, no unique way to specify their pole structures. Further, there is the difficulty of appearance of negative-norm states about them. As to their applications to the meson-meson scattering, a promising amplitude has been presented by Frampton,!) who has impo~ed a restraint on (an infinite number of) satellite terms using a symmetric group. The 7[7[-47[7[ Frampton amplitude (A 4(1) in his work) does not involve odd daughters, and it is presumably free from the difficulty of appearance of ghosts. Applications of the Veneziano-type models to the baryonmeson scattering have, however, faced more difficulties. In this respect, Hoyer and Uschersohn) have propo~ed a new method of imposing duality constraints recently. The scheme given by them is composed of an infinite number of localized duality relations which involve only observed resonances. According to the supposition that the dynamics of hadrons is governed essentially by the quark-orbital Regge trajectory, presented by Bando et al.) and Nakkagawa et al.) who studied the hadron dynamics and the hadron spectrum in the quark model, it is considered to be worth while to generalize the Hoyer-Uschersohn relation assuming the harmonic-oscillator spectrum of SU(6)@O(3)L multiplets for the idealized hadron spectrum. Such a generalization has been done by the author recently:) In fact, the obtained relation has been found to be successful for both of the baryon-meson and meson-meson scattering. About low-lying resonances, it has been shown to be consistent with experiments.) In this paper, we discuss the elastic resonance widths of highly excited mesons in the above scheme with the quark-model hadron spectrum. Our purpose is to examine whether or not the scheme is hopeful to the absence of negative· norm states. Let us consider the 0-0-4 0-0processes where the u-channel is exotic. The present scheme for the process under discussion is