  We present a purely diagrammatic derivation of the dual fermion scheme [Phys.
Rev. B 77 (2008) 033101]. The derivation makes particularly clear that a
similar scheme can be developed for an arbitrary reference system provided it
has the same interaction term as the original system. Thereby no restrictions
are imposed by the locality of the reference problem or by the nature of the
original problem as a lattice one. We present new arguments in favour of
keeping the dual denominator in the expression for the lattice self-energy
independently of the truncation of the dual interaction. As an example we
present the computational results for the half-filled 2D Hubbard model with the
choice of a $2\times2$ plaquette with periodic boundary conditions as a
reference system. We observe that obtained results are in a good agreement with
numerically exact lattice quantum Monte Carlo data.
