A New Upper Limit on the Decay $\eta\to e^{+}e^{-}$

We have searched for the rare decay of the eta meson $\eta \to e^{+}e^{-}$ using the CLEO II detector. The $\eta$'s were produced in $e^{+}e^{-}$ collisions with 10 GeV center-of-mass energy at the Cornell Electron Storage Ring (CESR). We find with 90% confidence the upper limit on the branching fraction $B(\eta \to e^{+}e^{-}) < 7.7\times 10^{-5}$. The application of conventional elementary particle theory to this decay predicts a branching fraction of about $10^{-9}$.