Most password-based key exchange protocols consider how to exchange a session key between a client and a server. Client-to-Client password authenticated key exchange protocol considers the scenario where two clients want to establish a session key but they only share their passwords with their own servers. In [1], Jin Wook Byun et al. proposed two such protocols called cross-realm C2C-PAKE and single-server C2C-PAKE. Recently some flaws of these two protocols are found and some improvements are suggested. In this paper, we show that the cross-realm C2C-PAKE protocol and its all improved forms are still insecure. And we also present a new cross-realm C2C-PAKE protocol which is resistant to all known attacks.