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Data taken with the CYGNUS detector between 1989 September and 1993 January have been used to search for 1-s bursts of ultrahigh-energy gamma rays from point sources at arbitrary locations in the northern sky. We find no evidence for such bursts. We set a theory-dependent upper limit on the rate-density of evaporating black holes of 8.5 x 10 exp 5/cu yr at the 99 percent C.L. When the same emission spectrum is used to recalculate previous upper limits based on direct searches, this limit is the most restrictive by nearly 2 orders of magnitude.