Modified N=1 Green-Schwarz superstring with irreducible first class constraints

We propose modified action which is equivalent to N=1 Green-Schwarz superstring and which allows one to realize the supplementation trick [26]. Fermionic first and second class constraints are covariantly separated, the first class constraints (1CC) turn out to be irreducible. We discuss also equations of motion in the covariant gauge for $\kappa$-symmetry. It is shown how the usual Fock space picture can be obtained in this gauge.