  The implications of the positivity constraint on the presently unknown
polarized structure function of the photon, $g_1^{\gamma}(x,Q^2)$, are studied
in detail. In particular the non-trivial consequences of this constraint,
$|g_1^{\gamma}(x,Q^2)|\leq F_1^{\gamma}(x,Q^2)$, in the next-to-leading order
analysis of $g_1^{\gamma}$ are pointed out by employing appropriate (DIS)
factorization schemes related to $g_1^{\gamma}$ and $F_1^{\gamma}$ (rather than
to $F_2^{\gamma}$).
