Based on $psi(3686)$ decays of 106 million, the 1.31 billion J/psi events and a data sample of $psi(3770)$ with $2.9~fb^{-1}$ integrated luminosity, many analyses are performed. Exclusively baryonic decays of the $psi(3770)$, the radiative transition $psi(3770)togammaeta_c(2S)$, the $psi(3770)$ transition to $chi_{cJ}$, isospin violation decay $chi_{c0,2}topi^0eta_c$, the $C-$parity violation decays $J/psitogammagamma,gammaphi$ are searched for, but no significant signals are observed, and upper limits are set for these decays. The decays of $psi(3770)togammachi_{c1}$ and $J/psitopi^0phi$ signals are observed. These measurements provide more information on the charmonium structure, and the isospin and $C$-parity violation in the charmonium decays.
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