  The Moutard transformation for a two-dimensional Dirac operator with a
complex-valued potential is constructed. It is showed that this transformation
relates the potentials of Weierstrass representations of surfaces related by a
composition of the inversion and a reflection with respect to an axis. It is
given an analytical description of an explicit example of such a transformation
which results in a creation of double points on the spectral curve of a Dirac
operator with a double-periodic potential.
