  We study the similarity renormalization scheme for hamiltonians to the fourth
order in perturbation theory using a model hamiltonian for fermions coupled to
bosons. We demonstrate that the free finite parts of counterterms can be chosen
in such a way that the T-matrix is covariant up to the fourth order and the
eigenvalue equation for the physical fermion reduces to the Dirac equation.
Through this choice, the systematic renormalization scheme reproduces the model
solution originally proposed by G{\l}azek and Perry.
