Client-to-client password authenticated key exchange (C2C-PAKE) protocol deals with the authenticated key exchange process between two clients, who only share their passwords with their own servers. Jin Wook Byun et al. first divided this scenario into two kinds called single-server C2C-PAKE protocol and cross-realm C2C-PAKE protocol respectively. Recently, Abdalla et al. proposed a generic construction for single-server C2C-PAKE protocol and presented a concrete example with security proof. But, no similar results about cross-realm C2C-PAKE protocol exist. In fact, all existing cross-realm C2C-PAKE protocols are found insecure. To counter flaws and provide a secure cross-realm C2C-PAKE protocol, in this paper, we introduce a formal model and corresponding security definitions. Then, a new cross-realm C2C-PAKE protocol is presented with security proof.