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As a consequence, an infinite set of independent algebras labeled by $\\rho$ corresponding to the conjugate classes of the {\\it outer} automorphism group SO(4)/SU(2)=SU(2) are obtained \\`a la Schwimmer and Seiberg. We construct Feigin-Fuchs representations with the $\\rho$ parameter embedded for the infinite set of the $N=4$ nonequivalent algebras. 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