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Recently, Hsueh and Chen [in Proceedings of the 14th Information Security Conference, National Taiwan University of Science and Technology, Taipei, pp. 236-242, ] proposed a quantum key agreement (QKA) protocol with maximally entangled states. Their protocol allows two users to negotiate a secret key in such a way that no one can predetermine the shared key alone. This study points out two security flaws in their protocol: (1) a legitimate but malicious user can fully control the shared key alone; (2) an eavesdropper can obtain the shared key without being detected. A possible solution is presented to avoid these attacks and also Tsai et al.'s CNOT attack [in Proceedings of the 20th Cryptology and Information Security Conference, National Chiao Tung University, Hsinchu, pp. 210-213, ] on Hsueh and Chen protocol to obtain the shared key without being detected. [ABSTRACT FROM AUTHOR]