We build up and analyze the constrained cohomology set-up for the anti-BRS
structure of the Witten's topological Yang-Mills field theory. We also disc
uss a conjecture on the existence of a novel class of topological observabl
es arising within the context of the anti-BRS differential algebra. The ant
i-BRS counterparts of the Witten's observables are then identifyed in terms
of the method of the spectral sequences.