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Since the original Cai-Li protocol [Chin. Phys. Lett. 21 (2004) 601] can be used only in an ideal quantum communication, we present the modified Cai-Li protocol that can be used in the a noisy quantum channel by using Calderbank-Shor-Steane (CSS) codes to correct errors. We also give a tight bound on the connection between information Eve eavesdropped with a measurement attack in line B → A and detection probability,which shows that the Cai-Li protocol can be used as a quasisecure direct quantum communication.