By using Password-based Authenticated Key Exchange (PAKE), a server can authenticate a user who has only the same password shared with the server in advance and establish a session key with the user simultaneously. However, in the real applications, we may have a situation where a user needs to share a session key with server A, but the authentication needs to be done by a different server B that shares the password with the user. Further, to achieve higher security on the server side, it may be required to make PAKE tolerant of a server breach by having multiple authentication servers. To deal with such a situation, Abdalla et al. proposed a variant of PAKE called Gateway Threshold PAKE (GTPAKE) where a gateway corresponds to the aforementioned server A being an on-line service provider and also a potential adversary that may try to guess the passwords. However, the schemes of Abdalla et al. turned out to be vulnerable to Undetectable On-line Dictionary Attack (UDonDA). In this paper, we propose the first GTPAKE provably secure against UDonDA, and in the security analysis, we prove that our GTPAKE is secure even if an adversary breaks into parts of multiple authentication servers.