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Abstract This paper studies the beamforming design for an active reconfigurable intelligent surface (RIS) aided non‐orthogonal multiple access (NOMA) network. It aims to minimize the transmission power while satisfying the requirement of the quality of service (QoS). To solve this problem, an iterative algorithm based on approximate transformations and penalty functions is proposed. Finally, simulation results illustrate that an active RIS‐aided NOMA system can achieve significant performance gains over the passive RIS‐aided NOMA network.