We discuss observations of the soft gamma repeater SGR 1806-20 during the RXTE Target of Opportunity observations made in November 1996. During the ~50 ksec RXTE observation, HEXTE (15-250 keV) detected 17 bursts from the source, with fluxes ranging from 3 x 10^{-9} to 2.2 x 10^{-7} ergs cm^{-2} s^{-1} (20-100 keV). We obtained spectra for the brighter HEXTE by fitting thermal bremsstrahlung and power law functions over the energy range 17 - 200 keV. The best-fit temperatures and photon indices range from 30 - 55 keV and 2.2 - 2.7, respectively. The weighted average temperature of the HEXTE bursts was 41.8 +/- 1.7 keV, which is consistent with previous SGR 1806-20 burst spectra. The persistent emission from SGR 1806-20 was not detected with HEXTE.
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