A deniable authentication protocol allows a sender to transfer an authenticated message to a receiver, and the receiver cannot prove to a third party about the source of the message. In 2006, Zhu et al. analyzed deniable authentication protocols proposed by Deng et al. in 2001, which were based on a protocol proposed by Aumann et al. in 1998. In this paper, we show that the modified protocols by Zhu et al. suffer from a Byzantine attack when two sessions run concurrently. We also suggest methods to solve the problem.