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This paper investigates a TCP proxy that splits a TCP connection into two parts consisting of a wireless link and a wired network. The TCP proxy is effective for improving TCP performance in such a heterogeneous network including a wireless link, on which transmission errors occur. This paper describes how the TCP proxy produces large size forward data due to a packet loss on the wireless link. It also identifies a new problem that the output traffic from the TCP proxy becomes bursty due to the large size forward data. To mitigate bursts of packets by the TCP proxy this paper proposes a scheme that the proxy performs a pacing function which places a gap between two consecutive packets. Since this function is performed in cooperation with the flow control between two TCP connections, the scheme has an advantage that it requires a small amount of forwarding buffers for the pacing. Simulation results using ns-2 show that bursty packets are produced by the conventional TCP proxy and the pacing function suppresses them. The results also show that throughput is improved by the proposed scheme, while the throughput of the conventional TCP proxy suffers from packet losses in the wired network due to the bursts of packets.