  In this revised version we correct some mistakes, realizing the supersymmetry
algebra on the exact S matrix, taking into account several phase factros. We
study the constraint imposed by supersymmetry on the exact $S$-matrix of
$\Complex P^{n-1}$ model, and compute a non-trivial phase factor in the
relation between the $S$-matrix and one of the supersymmetry generators. We
discuss several features connected with the physical interpretation of the
result. The supersymmetry current is studied in such context as well, and we
find some operators appearing in the conservation equation of the supersymmetry
current that might be connected with such phase factors. The relation with the
literature on the subject is also discussed. hep-th/yymmnnn
