SUSY transformations between diagonalizable and non-diagonalizable Hamiltonians

Recently (Samsonov B F and Roy P 2005 J. Phys. A: Math. Gen. 38 L249) an explicit example of a PT-symmetric non-diagonalizable Hamiltonian has been given. In this letter we show that such Hamiltonians appear as supersymmetric (SUSY) partners of Hermitian (hence diagonalizable) Hamiltonians and can be transformed back to diagonalizable forms by appropriate SUSY transformations.