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 PT 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. 1

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Theories with higher derivatives involve linear instabilities in the Hamiltonian commonly known as Ostrogradski ghosts and can be viewed as a very serious problem during quantization. To cure this, we have considered the properties of antilinearity that can be found inherently in the non-Hermitian Hamiltonians. Owing to the existence of antilinearity, we can construct an operator, called the V-operator, which acts as an intertwining operator between the Hamiltonian and its Hermitian conjugate. We have used this V-operator to remove the linear momentum term from the higher derivative Hamiltonian by making it non-Hermitian in the first place via an isospectral similarity transformation. The final form of the Hamiltonian is free from the Ostrogradski ghosts under some restriction on the mass term.