Using 482 pb$^{-1}$ of data taken at $sqrt{s}=4.009$ GeV, we measure the branching fractions of the decays of $D^{*0}$ into $D^0pi^0$ and $D^0gamma$ to be $BR(D^{*0} to D^0pi^0)=(65.5pm 0.8pm 0.5)%$ and $BR(D^{*0} to D^0gamma)=(34.5pm 0.8pm 0.5)%$ respectively, by assuming that the $D^{*0}$ decays only into these two modes. The ratio of the two branching fractions is $BR(D^{*0} to D^0pi^0)/BR(D^{*0} to D^0gamma) =1.90pm 0.07pm 0.05$, which is independent of the assumption made above. The first uncertainties are statistical and the second ones systematic. The precision is improved by a factor of three compared to the present world average values.
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