Search for the Decay $D^0 \rightarrow \omega \eta$

We present a preliminary result of the search for the decay $D^0 \rightarrow \omega \eta$ where $D^0$ comes from the decay $D^{*+} \rightarrow D^0 \pi^+$. We use a high statistics data sample collected with the BaBar detector at the PEP-II asymmetric $e^{+} e^{-}$ collider at SLAC.