We describe a search of archival data from the Burst and Transient Source Experiment (BATSE). The purpose of the search is to find astronomically interesting transients that did not activate the burst detection (or ``trigger) system onboard the spacecraft. Our search is sensitive to events with peak fluxes (on the 1.024 s time scale) that are lower by a factor of 2 than can be detected with the onboard burst trigger. In a search of 345 days of archival data, we detected 91 events in the 50--300 keV range that resemble classical gamma ray bursts but that did not activate the onboard burst trigger. We also detected 110 low-energy (25--50 keV) events of unknown origins which may include activity from SGR 1806-20 and bursts and flares from X-ray binaries. This paper gives the occurrence times, estimated source directions, durations, peak fluxes, and fluences for the 91 gamma ray burst candidates. The direction and intensity distributions of these bursts imply that the biases inherent in the onboard trigger mechanism have not significantly affected the completeness of the published BATSE gamma ray burst catalogs.
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