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The effect of the parity nonconserving nuclear force on the 501-keV y transition of 80Hf has been confirmed by a remeasurement of the angular distribution asymmetry of the radiation emitted by~H f~polarized at temperatures down to 16 mK. A difference of 1% was observed between the p-ray intensities parallel and antiparall. el to the nuclear polarization direction. When the results of the present study are averaged with previous nuclear polarization experiments and compared with the results of circular polarization experiments, it is deduced that the parity mixing can be uniquely assigned to an irregular &2 multiple, rather than to a higher order irregular multiple such as M3. Assuming a vanishing M3 component, the present study yieMs~= (E2)/(M2) = -0.026+ 0.002, and the global average from all measurements is e= -0.030 + 0.002.