Abstract
We show that when the algebra of gauge transformations is not closed one can still generally define an effective action that is invariant under an appropriate extension of the Becchi-Rouet-Stora transformations. Both the action and transformation rules contain terms of higher order in the ghost fields. The generalized Ward identifies imply the existence of a gauge-independent S matrix. Nilpotency of extended BRS transformations is regained upon use of the full field equations of ghost and ordinary fields.
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