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This paper proposes a spectrum resource reduction method using a hybrid ARQ for OFDM cellular system by relaying the required data with error from the relay station. In this system, we consider a direct communication from a base station to a mobile station using OFDM cellular system like WiMAX and a relayed network from the relay station to the mobile station using highly reliable short range network like wireless LAN. In order to reduce the spectrum resource from the base station to the mobile station by using the relay station, we apply an adaptive rate control and an adaptive retransmission control based on a Hybrid ARQ by using a punctured convolutional code. The proposed method controls the coding rate transmitted from the base station by checking two kinds of the channel status one is from the base station to the relay station, and the other one is from the base station to the mobile station.