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Compared to Wireless Sensor Network (WSN), Body Area Network (BAN) has its own unique requirements and further, it is more difficult to equip the medical sensors with replaceable batteries as this reduces the comport of the person wearing them. In this respect, a lot of efforts are being made by 802.15.6 WG to standardize a more efficient Medium Access Control (MAC) for BAN. Thus, in this paper, we propose an energy-efficient MAC scheme designed for BAN. The main idea is to allow for body sensors to transmit their data to the coordinator using multi-hop transmission in the BAN with the aim to maximize the lifetime of BAN. The performance of the proposed MAC scheme is evaluated by computer simulations in terms of lifetime and resource utilization.