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IPv6 offers significant advantages over the current IPv4, however it will take long time to replace IPv4 with IPv6. Therefore, these two protocols are expected to coexist during the transition period. A number of transition mechanisms are proposed by IETF Next Generation Transition Working Group. However, most of them provide only the mechanism to initiate sessions from hosts within the IPv6 network to those within the IPv4 network, but do not support the initiation from IPv4 hosts to IPv6 ones. In this paper, we propose the IPv4-to-IPv6 dual stack transition mechanism (4to6 DSTM) which can operate even in the case that hosts in the IPv4 network initiate connections within hosts in the IPv6 network.