With proliferation of the Internet and its services, how to provide stable and efficient Internet services via reliable high-speed network has become an important issue. Multihomed network is attracted much attention to provide stable and efficient Internet services. In this paper, we focus on the multihoming method in the IPv6 environment. In the IPv6 environment, each host can be assigned multiple IP addresses from different ISPs on one network interface, thus the multihoming is relatively easier than that in the IPv4 environment. However, since many ISPs adopt ingress filtering for security concerns, a multihomed site should select a proper site-exit router according to the source IP address of the packet to communicate with the outside the site successfully. In most site-exit router selection methods, a kind of source IP address dependent routing method is introduced which has some problems in terms of high deployment cost and lack of fault-tolerance and so on.In this paper, we propose a new site-exit router selection method using the routing header which can indicate the router to pass through in the IPv6 environment. This method introduces two middlewares, one into the inside server and the other into the site-exit router. The one in the inside server attaches a routing header which indicates a specific site-exit router to pass through according to the source IP address of the packet, and the other in the site-exit router removes the attached routing header from the packet, thus the inside server can communicate with the outside the site successfully as usual. We also implemented a prototype system including the proposed inside server and the site-exit router and performed feature evaluation as well as performance evaluation. From the evaluation results, we confirmed the proposed method worked well and the overhead of the middlewares are acceptable for practical use in the real network environments.