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In this paper, we proposed a proportional fair (PF) scheduling algorithm for systems with multiple carriers such as orthogonal frequency division multiple access systems. The scheduler assigns users to carriers to maximize the sum of logarithmic transmission rate, which is compatible with the definition by RE Kelly (Journal Operational Research Soc., vol.49, p.237-252, 1998). It is shown that the PF scheduling in the high data rate (HDR) system proposed by Qualcomm is a special case of our proposed scheme. A simple system is presented, which proves its superiority over other schemes for multicarrier transmission, e.g. extended round robin and the PF scheduling scheme for the HDR system.