  We reconsider the classical problem of the continuation of degenerate
periodic orbits in Hamiltonian systems. In particular we focus on periodic
orbits that arise from the breaking of a completely resonant maximal torus. We
here propose a suitable normal form construction that allows to identify and
approximate the periodic orbits which survive to the breaking of the resonant
torus. Our algorithm allows to treat the continuation of approximate orbits
which are at leading order degenerate, hence not covered by classical averaging
methods. We discuss possible future extensions and applications to localized
periodic orbits in chains of weakly coupled oscillators.
