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In this paper, we propose a packet scheduling algorithm for cellular relay networks by considering relay selection, variation of channel quality, and packet delay. In the networks, mobile users are equipped with not only cellular but also user relaying radio interfaces, where base station exploits adaptive high speed downlink channel. Our proposed algorithm selects a user with good cellular channel condition as a relay station for other users with bad cellular channel condition but can get access to relay link with good quality. This can achieve flexible packet scheduling by adjusting transmission rates of cellular link. Packets are scheduled for transmission depending on scheduling indexes which are calculated based on user's achieved transmission rate, packet utility, and proportional fairness of their throughput. The performance results obtained by using computer simulation show that the proposed scheduling algorithm is able to achieve high network capacity, low packet loss, and good fairness in terms of received throughput of mobile users.