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Jet event rates in deep inelastic ep scattering at HERA are investigatedapplying the modified JADE jet algorithm. The analysis uses data taken with theH1 detector in 1994 and 1995. The data are corrected for detector andhadronization effects and then compared with perturbative QCD predictions usingnext-to-leading order calculations. The strong coupling constant alpha_S(M_Z^2)is determined evaluating the jet event rates. Values of alpha_S(Q^2) areextracted in four different bins of the negative squared momentumtransfer~$\qq$ in the range from 40 GeV2 to 4000 GeV2. A combined fit of therenormalization group equation to these several alpha_S(Q^2) values results inalpha_S(M_Z^2) = 0.117+-0.003(stat)+0.009-0.013(syst)+0.006(jet algorithm).Comment: 17 pages, 4 figures, 3 tables, this version to appear in Eur. Phys.  J.; it replaces first posted hep-ex/9807019 which had incorrect figure 4

Multi-jet event rates in deep inelastic scattering and determination of the strong coupling constant