Constructing real canonical forms of Hamiltonian matrices with two imaginary eigenvalues

If $A$ is a Hamiltonian matrix and $P$ a symplectic matrix then the product $P^{-1}AP$ is a Hamiltonian matrix. In this paper we consider the case where the matrix $A$ has a pair of imaginary eigenvalues and develop an algorithm which finds a matrix $P$ such that the matrix $P^{-1}AP$ has a particularly simple form, a canonical form.