  The Hamiltonian renormalisation programme motivated by constructive QFT and
Osterwalder-Schrader reconstruction which was recently launched for bosonic
field theories is extended to fermions. As fermion quantisation is not in terms
of measures, the scheme has to be mildly modified accordingly.
  We exemplify the scheme for free fermions both for compact and non-compact
spatial topologies respectively (i.e. with and without IR cut-off) and
demonstrate that the convenient Dirichlet or Shannon coarse graining kernels
recently advertised in a companion paper lead to a manifestly doubler free
flow.
