  The discrete non-commutative Darboux system of equations with self-consistent
sources is constructed, utilizing both the vectorial fundamental (binary
Darboux) transformation and the method of additional independent variables.
Then the symmetric reduction of discrete Darboux equations with sources is
presented. In order to provide a simpler version of the resulting equations we
introduce the $\tau/\sigma$ form of the (commutative) discrete Darboux system.
Our equations give, in continuous limit, the version with self-consistent
sources of the classical symmetric Darboux system.
