The modified version of Yahalom protocol improved by Burrows, Abradi, and Needham (BAN) still has security drawbacks. This study analyzed such flaws in a detailed way from the point of strand spaces, which is a novel method of analyzing protoeol's security. First, a mathematical model of BAN-Yahalom protocol is constructed. Second, penetrators' abilities are restricted with a rigorous and formalized definition. Moreover, to increase the security of this protocol against potential attackers in practice, a further improvement is made to the protocol. Future application of this re-improved protocol is also discussed.