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We present a measurement of the branching fractions for the Cabibbo-favoredradiative decay, $D^{0} \to {\bar K}^{*0} \gamma$, and the Cabibbo-suppressedradiative decay, $D^{0} \to \phi \gamma$. These measurements are based on adata sample corresponding to an integrated luminosity of $387.1 fb^{-1}$,recorded with the BaBar detector at the PEP-II $e^+e^-$ asymmetric-energycollider operating at center-of-mass energies 10.58 and 10.54 GeV. We measurethe branching fractions relative to the well-studied decay $D^{0} \to K^{-}\pi^{+}$ and find ${\cal B}(D^{0} \to {\bar K}^{*0} \gamma)/{\cal B}(D^{0} \toK^{-} \pi^{+}) = (8.43 \pm 0.51 \pm 0.70) \times 10^{-3}$ and ${\cal B}(D^{0}\to \phi \gamma)/{\cal B}(D^{0} \to K^{-} \pi^{+}) = (7.15 \pm 0.78 \pm 0.69)\times 10^{-4}$, where the first error is statistical and the second issystematic. This is the first measurement of ${\cal B}(D^{0} \to {\bar K}^{*0}\gamma)$.

Measurement of the Branching Fractions of the Radiative Charm Decays $D^{0} \to {\bar K}^{*0} \gamma$ and $D^{0} \to \phi \gamma$