  We harness the freedom in the celebrated gauge transformation approach to
generate dark solitons of coupled nonlinear Schr\"odinger (NLS) type equations.
The new approach which is purely algebraic could prove to be very useful,
particularly in the construction of vector dark solitons in the fields of
nonlinear optics, plasma physics and Bose-Einstein condensates. We have
employed this algebraic method to coupled Gross- Pitaevskii (GP) and NLS
equations and obtained dark solitons.
