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Worm detection system must detect worms efficiently and effectively. Current detection methods are mainly based on the property of low successful connections rate of worms. However, they may neglect worms if worms insert successful connections deliberately. Because the size in packets or bytes of normal TCP connections is heavy-tailed, we present a detection method by combining detection criteria of failed connections and heavy-tailed distribution of connection size for a given local host. It is more difficult for worms to evade. The method can decrease false negative and positive rates. The experiments show that our method can detect scanning worms with high efficiency and effectiveness.