In recent issue of Journal of Applied Mathematics and Computation (2005), Lee, Kim, & Yoo revealed an attack on Hsu, Wu, & Wu (2003) authenticated key agreement protocol, and then presented an improved protocol. However, Lee, Kim, & Yoo (2005) present only heuristic argument with no formal proof of security. In this work, we revealed previously unpublished flaw in the protocol. We may speculate that such errors could have been found by protocol designers if proofs of security were to be constructed, and hope this work will encourage future protocol designers to provide proofs of security. We conclude with a countermeasure due to Choo, Boyd, & Hitchcock (2005).