Analyzing correlation functions of charmonia at finite temperature ($T$) on $32^3times(32-96)$ anisotropic lattices by the maximum entropy method (MEM), we find that $J/psi$ and $eta_c$ survive as distinct resonances in the plasma even up to $T simeq 1.6 T_c$ and that they eventually dissociate between $1.6 T_c$ and $1.9 T_c$ ($T_c$ is the critical temperature of deconfinement). This suggests that the deconfined plasma is non-perturbative enough to hold heavy-quark bound states. The importance of having sufficient number of temporal data points in MEM analyses is also emphasized.