  We consider the quark-antiquark Green's function in the Schwinger Model with
instanton contributions taken into account. Thanks to the fact that this
function may analytically be found, we draw out singular terms, which arise due
to the formation of the bound state in the theory -- the massive Schwinger
boson. The principal term has a pole character. The residue in this pole
contains contributions from various instanton sectors: $0,\pm 1, \pm 2$. It is
shown, that the nonzero ones change the factorizability property. The formula
for the residue is compared to the Bethe-Salpeter wave function found as a
field amplitude. Next, it is demonstrated, that apart from polar part, there
appears in the Green's function also the weak branch point singularity of the
logarithmic and dilogarithmic nature. These results are not in variance with
the universally adopted $S$-matrix factorization.
