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Invariant (nonplanar) anomaly of noncommutative QED is reexamined in this paper. It is found that just as in ordinary gauge theory UV regularization is needed to discover anomalies, in noncommutative case, in addition, an IR regularization is also required to exhibit the existence of invariant anomaly. Thus resolving the controversy in the value of invariant anomaly, an expression for the unintegrated anomaly is found. Schwinger terms of the current algebra of the theory are derived.