  We re-examine the geometry and algebraic structure of BRST's of Topological
Yang-Mills theory based on the universal bundle formalism of Atiyah and Singer.
This enables us to find a natural generalization of the {\it Russian formula
and descent equations\/}, which can be used as algebraic method to find the
non-Abelian anomalies counterparts in Topological Yang-Mills theory. We suggest
that the presence of the non-Abelian anomaly obstructs the proper definition of
Donaldson's invariants.
