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The consistent performance, energy efficiency, and reliability are important factors for real-time monitoring of a patient's data, especially in a hospital environment. In this paper a routing protocol is proposed by considering the Quality of Service requirements of the body area network data packets. A mechanism for handling delay-sensitive packets is provided by this protocol. Extensive simulations using OMNeT++ based simulator Castalia illustrate that the proposed algorithm provides better performance than other QoS-aware routing protocols in terms of higher successful transmission rates, lower overall network traffic load, and fewer number of packet timeouts in both the mobile and static patient scenarios.