  The QCD higher order effects to the polarized structure function $g_2(x, Q^2
)$ are reanalyzed for massive quarks in the context of the operator product
expansion. We confirm that the lowest moment of $g_2 (x, Q^2 )$ which
corresponds to the Burkhardt-Cottingham sum rule does {\sl not} suffer from
radiative corrections in perturbative QCD.
