With the emergence of bandwidth-greedy application services, high-speed transport protocols are expected to effectively and aggressively use large amounts of bandwidth in current broadband and multimedia networks. However, when high-speed transport protocols compete with other standard TCP flows, they can occupy most of the available bandwidth leading to disruption of service. To deploy high-speed transport protocols on the Internet, such unfair situations must be improved. In this paper, therefore, we propose a method to improve fairness, called Kyushu-TCP (KTCP), which introduces a non-aggressive period in the congestion avoidance phase to give other standard TCP flows more chances of increasing their transmission rates. This method improves fairness in terms of the throughput by estimating the stably available bandwidth-delay product and adjusting its transmission rate based on this estimation. We show the effectiveness of the proposed method through simulations.