Canonical covariant formulation of Green-Schwarz superstring without second class constraints

We describe a canonical covariant formulation of the Green-Schwarz superstring which allows the construction of a new covariant action canonically equivalent to the Green-Schwarz action but subjected only to first class constraints. From this action the correct BRST operator for the quantization of the Green-Schwarz superstring may be constructed. Also the gauge fixed action in the light-cone gauge may be reobtained. The action presented in this letter generalizes in a non-trivial form the action introduced by Kallosh for the Brink-Schwarz-Casalbuoni superparticle.