  Following our previous work, a complete classical solution of the CGHS model
in Hamiltonian formulation in new variables is given. We preform a series of
analyses and transformations to get to the CGHS Hamiltonian in new variables
from a generic class of two dimensional dilatonic gravitational systems coupled
to matter. This gives us a second class system, a total Hamiltonian consisting
of a Hamiltonian constraint, a diffeomorphism constraint and two second class
constraints. We calculate the Dirac brackets, bring them to a standard form
similar to the Poisson brackets by introducing a new variable. Then by
rescaling lapse and shift, the Hamiltonian constraint is transformed into a
form where it has an strong Abelian algebra with itself. This property holds
both in vacuum case and in case with matter coupling. Then for each of the
vacuum and the coupled-to-matter cases, we preform two gauge fixings, one set
for each case, and solve the classical system completely in both cases. The
gauge fixing of the case coupled to matter is done by implementing a method
based on canonical transformation to a new set of variables and leads to a true
local Hamiltonian. We also show that our formalism is consistent with the
original CGHS paper by showing that the equations of motion are the same in
both cases. Finally we derive the relevant surface term of the model.
