  Using 58 million $J/\psi$ events taken with the BESII detector, a search for
$eta_{c}$ CP violating decays into $\pi\pi$ and $\bar{K}K$ has been performed.
No clear $eta_{c}$ is observed, and upper limits for $B(eta_{c}->\pi \pi)$and
$B(eta_{c}->\bar{K} K)$ are given at the 90% confidence level,
$B(J/\psi->\gamma\eta_{c})\times B(eta_{c}->\pi^{+}\pi^{-})<1.1\times 10^{-5}$
, $B(J/\psi->\gamma\eta_{c})\times B(eta_{c}->\pi^{0}\pi^{0})<0.71\times
10^{-5}$, $B(J/\psi->\gamma\eta_{c})\times B(eta_{c}->K^{+}K^{-})<0.96\times
10^{-5}$ and $B(J/\psi->\gamma\eta_{c})\times
B(eta_{c}->{K_{s}}^{0}{K_{s}}^{0})<0.53\times 10^{-5}$.
