We have conducted a search for emission from the 70.7→61.3 rotational-torsional transition of stratospheric hydrogen peroxide at 270.610 GHz, using a ground-based millimeter-wave heterodyne receiver which has been used successfully to measure stratospheric ClO, HO2, HCN and other trace gases. Observations were made at Mauna Kea, Hawaii (19.5¿N) in late May and early June of 1983. No definitive signal was detected in the output of a 256-channel filter band spectrometer. From this result we deduce an upper limit on the H2O2 mixing ratio between approximately 30 and 50 km altitude which is approximately 2 times that predicted from a recent stratospheric model by Sze and Ko. Towards its middle altitude range, this limit overlaps a recent upper limit set by K. V. Chance and W. A. Traub (1984) between 22 and 38 km and is ~2¿ lower in the mixing ratio at 32 km than that implied by a tentative H2O2 detection by J. W. Waters et al. (1981).