BRS anomaly in the fully quantized non-abelian gauge theory

The form of a possible anomalous term in Slavnov-Taylor identities of Yang-Mills theory is determined by making use of a cohomological exact sequence and the same method is applied to the theory with an anti-symmetric tensor gauge field. In both cases the unique anomalous term has the same form as the conventional non-abelian anomaly. The effect of the anomaly on the nilpotency of the BRS transformation is discussed also.