  A renormalization scheme for interacting fermionic systems is presented where
the renormalization is carried out in terms of the fermionic degrees of
freedom. The scheme is based on continuous unitary transformations of the
hamiltonian which stays hermitian throughout the renormalization flow, whereby
any frequency dependence is avoided. The approach is illustrated in detail for
a model of spinless fermions with nearest neighbour repulsion in one dimension.
Even though the fermionic degrees of freedom do not provide an easy starting
point in one dimension very good results are obtained which agree well with the
exact findings based on Bethe ansatz.
