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We calculate the rate for $e^+e^-$ annihilation into four jets atnext-to-leading order in perturbative QCD, but omitting terms that aresuppressed by one or more powers of $1/\Nc^2$, where $\Nc$ is the number ofcolors. The $\cO(\alpha_s^3)$ corrections depend strongly on the jet resolutionparameter $\ycut$ and on the clustering and recombination schemes, and theysubstantially improve the agreement between theory and data.Comment: LaTex, 7 pages with 3 encapsulated figures. Minor changes and  references adde

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Electron-Positron Annihilation into Four Jets at Next-to-Leading Order inαs