With shortest path bridging MAC (SPBM), shortest path trees are computed based on link metrics from each node to all other participating nodes. When an edge bridge receives a frame, it selects a path along which to forward the frame to its destination node from multiple shortest paths. Blocking ports are eliminated to allow full use of the network links. This approach is expected to use network resources efficiently and to simplify the operating procedure. However, there is only one multipath distribution point in the SPBM network. This type of network can be defined as an end-to-end multipath network. Edge bridges need to split flows to achieve the load balancing of the entire network. This paper proposes a rate-based path selection scheme that can be employed for end-to-end multipath networks including SPBM. The proposed scheme assumes that a path with a low average rate will be congested because the TCP flow rates decrease on a congested path. When a new flow arrives at an edge bridge, it selects the path with the highest average rate since this should provide the new flow with the highest rate. The performance of the proposed scheme is confirmed by computer simulations. The appropriate timeout value is estimated from the expected round trip time (RTT). If an appropriate timeout value is used, the proposed scheme can realize good load balancing. The proposed scheme improves the efficiency of link utilization and throughput fairness. The performance is not affected by differences in the RTT or traffic congestion outside the SPBM network.