  We consider the quadratic supersymmetric aspect of the Darboux transformation
for the Green functions of the one-dimensional Dirac equation with a
generalized form of the potential. We obtain the relation between the initial
and the transformed Green functions on the whole real line. We also construct
the formula for the unabridged trace of the difference of the transformed and
the initial Green functions of the boundary problem on the whole real line. We
present an example illustrated our developments.
