We describe a search of archival data from the Burst and Transient Sou
rce Experiment (BATSE). The purpose of the search is to find astronomi
cally interesting transients that did not activate the burst-detection
(or ''trigger'') system on board the spacecraft. Our search is sensit
ive to events with peak fluxes (on the 1.024 s timescale) that are low
er by a factor of similar to 2 than can be detected with the on-board
burst trigger. In a search of 345 days of archival data, we detected 9
1 events in the 50-300 keV range that resemble classical gamma-ray bur
sts but that did not activate the on-board burst trigger. We also dete
cted 110 low-energy (25-50 keV) events of unknown origin that may incl
ude activity from soft gamma repeater (SGR) 1805-20 and bursts and fla
res from X-ray binaries. This paper gives the occurrence times, estima
ted 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 on-board trigg
er mechanism have not significantly affected the completeness of the p
ublished BATSE gamma-ray burst catalogs.