  The Ostrogradski ghost problem that appears in higher derivative theories
containing constraints has been considered here. Specifically we have
considered systems where only the second class constraints appear. For these
kind of systems, it is not possible to gauge away the linear momenta that cause
the instability. To solve this issue, we have considered the PT symmetric
aspects of the theory. As an example we have considered the Galilean invariant
Chern Simons model in $2+1$ D which is a purely second class system. By solving
the constraints, in the reduced phasespace, we have derived the \p similarity
transformed Hamiltonian and putting conditions on we found that the final form
of the Hamiltonian is free from any linear momenta and bounded from below.
