  The covariant and kappa-symmetric action for superstring in direct product of
two flat D=10 N=1 superspaces is presented. It is given by the sum of
supersymmetric generalization of two copies of chiral boson actions constructed
with the use of the Pasti-Sorokin-Tonin (PST) technique. The chirality of 8
`left' bosons and 8 `left' fermions and the anti-chirality of their `right'
counterparts are obtained as gauge fixed version of the equations of motion, so
that the physical degrees of freedom are essentially those of the II
Green-Schwarz superstring. Our action is manifestly T-duality invariant as the
fields describing oscillating and winding modes enter it on equal footing.
