We present measurements of an altitude-dependent upper limit for stratospheric hydrogen peroxide that is substantially lower than previously determined limits. The data were obtained with a remote-sensing far-infrared spectrometer during a balloon flight on 23 January 1983. Our 2 sigma upper limit is 0.05 ppbv near 26.5 km, and is large above and below that altitude. This new upper limit is compared with two currently available modeling calculations for H2O2; in the neighborhood of 32 km, it is slightly lower than, but comparable to these theoretical profiles. The implicaions for measurement of H2O2 at different latitudes and seasons are briefly discussed.