In body area networks (BANs), a node placed near the hub has a significant signal strength advantage. This issue, known as near-far problem, indicates that a near node may serve as a relay for a far node. Currently, the established orthogonal multiple access (OMA) requires the allocation of a specific resource block to a single node. In contrast, the emerging non-orthogonal multiple access (NOMA) allows simultaneous transmissions and uses successive interference cancellation (SIC) to recover the signals. For the first time in the literature, we introduce NOMA in BANs, to allow simultaneous transmissions from two nodes at a time, with distinguishable power levels. The crucial part of this technique is the dynamic pairing of the nodes by the hub. First, we review the fundamentals of uplink NOMA and we propose an access protocol in compliance with IEEE 802.15.6-2012, which combines random OMA with scheduled NOMA. Next, we propose three node pairing strategies, namely a random, a correlative and a conditional one, to meet the requirements of several applications. These strategies are evaluated with packet level simulations in OMNeT++. Our results show that the proposed scheme outperforms the basic OMA scheme at high packet rates and provides a feasible direction for novel relay-based applications.