  We have modified the colour screening theory of Chu and Matsui by properly
incorporating bag model equation of state for quark gluon plasma (QGP). We have
also chosen the pressure parametrization rather than parametrizing energy
density in the transverse plane. We assume that the QGP dense medium is
expanding in the longitudinal direction obeying Bjorken boost invariant scaling
law. Sequential melting of $\chi_c$, $\psi^{'}$ and $J/\psi$ is also considered
in this scenario. We have applied above formulation to the recent PHENIX
experimental data of $J/\psi$ suppression in Au + Au collisions at RHIC. We
find that the model gives a good description of data at mid-rapidity in terms
of survival probability versus number of participants without any necessity of
implementing (3+1)-dimensional expansion of the deconfined medium.
