Summary: Recently D. Chu, X. Liu and V. Mehrmann [Numer. Math. 105, No. 3, 375–412 (2007; Zbl 1116.65043)] developed an \(O(n^3)\) structure preserving method for computing the Hamiltonian real Schur form of a Hamiltonian matrix. This paper outlines an alternative derivation of the method and an alternative explanation of why the method works. Our approach places emphasis on eigenvalue swapping and relies less on matrix manipulations.