We propose a TCP window-size delegation method for downlink TXOP (transmission opportunity) Exchange in wireless local area networks (WLANs). In our method, the 'compliant' stations (STAs) cooperatively use their available bandwidth in accordance with their throughput demand. We realize our method only with minimal modifications of the TCP functions of a proxy server, which lets one station (the TXOP provider) delegate TCP window size to another station (the TXOP client) so that the provider delegates its TXOPs in WLANs to the client. Our method enables an STA to flexibly delegate TXOPs to another STA without adversely affecting the legacy STAs, which is confirmed by computer simulations. We also confirmed that our method requires no modification to legacy access points and STAs.