When you discretized a continuous time linear Hamiltonian system you may expect that the result will be a discrete time Hamiltonian system, However this is not always true. In this paper we compare the following methods: Forward Euler, Backward Euler, Pole-Zero matching and Zero-order hold, in order to see which one preserves the Hamiltonian property. The Rasvan's procedure preserves the Hamiltonian property However Rasvan uses two methods to discretize one system; in this work we want to use only one method to the whole system.