The Green-Schwarz superstring action is modified to include some set of additional (on-shell trivial) variables. A complete constraint system of the theory turns out to be reducible both in the original and in additional variable sectors. The initial 8s first class constrainst and 8c second class ones are shown to be unified with 8c first class and 8s second class constraints from the additional variables sector, resulting in SO(1,9)-covariant and linearly independent constraint sets. Residual reducibility proves to fall on second class constraints only.