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High-speed networks with large delays present a unique environment where TCP may have a problem utilizing the full bandwidth. Several congestion control proposals have been suggested to remedy this problem. The existing protocols consider mainly two properties: TCP friendliness and bandwidth scalability. That is, a protocol should not take away too much bandwidth from standard TCP flows while utilizing the full bandwidth of high-speed networks. This work presents another important constraint, namely, RTT (round trip time) unfairness where competing flows with different RTTs may consume vastly unfair bandwidth shares. Existing schemes have a severe RTT unfairness problem because the congestion window increase rate gets larger as the window grows ironically the very reason that makes them more scalable. RTT unfairness for high-speed networks occurs distinctly with drop tail routers for flows with large congestion windows where packet loss can be highly synchronized. After identifying the RTT unfairness problem of existing protocols, This work presents a new congestion control scheme that alleviates RTT unfairness while supporting TCP friendliness and bandwidth scalability. The proposed congestion control algorithm uses two window size control policies called additive increase and binary search increase. When the congestion window is large, additive increase with a large increment ensures square RTT unfairness as well as good scalability. Under small congestion windows, binary search increase supports TCP friendliness. The simulation results confirm these properties of the protocol.