  Dissociation temperatures of J/\psi, \psi', and \chi_c states play key roles
in the sequential J/\psi suppression scenario for high energy heavy ion
collisions. We report on a study of charmonium dissociation temperatures in
quenched lattice QCD. On anisotropic lattices, we first subtract the effects of
the constant mode in finite temperature meson correlators, which have lead to
unphysical results in previous studies. We then extract ground and first exited
state masses by diagonalizing correlation functions among different source and
sink operators. To distinguish bound states from scattering states, we first
compare the charmonium mass spectra under different spatial boundary
conditions, and examine the shape and the volume-dependence of their
Bethe-Salpeter wave functions. From these studies, we found so far no sign of
scattering states up to about 2.3T_c.
