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We have performed a search for radiative b-hadron decays using events produced in pp̅ collisions at √s=1.8 TeV and collected by the Collider Detector at Fermilab. The decays we considered were B̅d0→K*0(→K-π+) γ, B̅s0→φ(→K+K-) γ, Λb0→ Λ(→pπ-) γ, and their charge conjugates. Two independent methods to identify photons from such decays were employed. In the first method, the photon was detected in the electromagnetic calorimeter. In the second method, the photon was identified by an electron-positron pair produced through the external photon conversion before the tracking detector volume. By combining the two methods we obtain upper limits on the branching fractions for the Bd0, B̅s0, and Λb0 radiative decays which, at the 95% confidence level, are found to be B( B̅d0→K*0 γ)<1.4×10-4, B(B̅s0→φ γ)<1.6×10-4, and B( Λb0→ Λ γ)<1.9×10-3.