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Abstract Reconfigurable intelligent surface (RIS) has emerged as a promising technique for enhancing the performance of wireless networks. However, the traditional reflecting‐only RIS requires that the transmitter and receiver ought to be on the same side of the RIS, limiting the flexibility of RIS deployment. To overcome this drawback, a new simultaneous transmission and reflection reconfigurable intelligent surface (STAR‐RIS) has been proposed. Different from STAR‐RIS assisted half‐duplex systems in the existing literature, this work investigates a novel STAR‐RIS aided full‐duplex (FD) communication system. An FD base station (BS) communicates with an uplink (UL) user and a downlink user simultaneously over the same time‐frequency dimension assisted by a STAR‐RIS. The authors aim to maximise the energy efficiency by jointly optimising the transmit power of the BS and the UL user and the passive beamforming at the STAR‐RIS. The authors decouple the non‐convex problem into two subproblems and optimise them iteratively. The Dinkelbach's method is used to solve the power optimisation subproblem, whereas the penalty‐based method and successive convex approximation are applied to design the passive beamforming. The convergence and complexity of the proposed algorithm are also analysed. The simulation results demonstrate the superior performance of the proposed scheme compared with other baseline schemes.