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We propose a hybrid ARQ (HARQ) scheme for which a rate-1/2 error-correcting code with code length equal to the packet length is used in the HARQ operation, where each packet comprises two subpackets of equal lengths. For the HARQ system with constant packet lengths, the utilization of subpackets enables the flexibility of carrying new message (or data) in the retransmissions. Hence, such a system can gain additional throughput as compared to the system using all-redundancy retransmissions under the conditions of moderate to high signal-to-noise ratios (SNR). In the proposed HARQ scheme, each of the subpackets can be chosen as a data part, or a redundancy part, or a function of two subpackets, where the data part or the redundancy part may belong to different codewords of the rate-1/2 error-correcting code. With a proper design of the function subpacket, we can adaptively control the error-correcting capability used in the HARQ operation. The key idea is that there is possibility of recovering three data subpackets in one retransmission and hence increasing the throughput. The price is that in each retransmission, up to three bits are needed in the feedback channel to indicate which subpacket is successfully recovered.