  We introduce the covariant forms for the non-Abelian anomaly counterparts in
topological Yang-Mills theory, which satisfies the topological descent equation
modulo terms that vanish at the space of BRST fixed points. We use the
covariant anomalies as a new set of observables, which can absorb both $\dw$
and $\db$ ghost number violations of zero-modes. Then, we study some problems
due to the zero-modes originated from the reducible connections.
