  We show here that matrix Darboux-Toda transformation can be written as a
product of a number of mappings. Each of these mappings is a symmetry of the
matrix nonlinear Shrodinger system of integro-differential equations. We thus
introduce a completely new type of discrete transformations for this system.
The discrete symmetry of the vector nonlinear Shrodinger system is a particular
realization of these mappings.
