A deficit of atmospheric νμ events, consistent with the hypothesis of neutrino oscillations, is observed in the 5.90 kiloton-year fiducial exposure of the Soudan 2 detector. An unbinned maximum likelihood analysis of the neutrino LIE distribution has been carried out using the Feldman-Cousins prescription. The probability of the no oscillation hypothesis is 5.8×10-4. The 90% confidence allowed region in the sin 22θ,Δm2 plane is presented. The region includes the 90% confidence allowed region of the Super-K experiment.