  Over the last decades the 'fixed-node method' has been used for a numerical
treatment of thermodynamic properties of strongly correlated Fermi systems. In
this work correctness of the 'fixed -node method' for ideal Fermi systems has
been analytically analyzed. It is shown that the 'fixed-node' prescription of
calculation of the density matrix leads to contradictions even for two ideal
fermions. The main conclusion of this work is that the 'fixed-node method' can
not reproduce the fermion density matrices and should be considered as
uncontrolled empirical approach in treatment of thermodynamics of Fermi
systems.
