Analyzing correlation functions of charmonia at finite temperature (\(T\)) on \(32^3\times(32-96)\) 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.