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In this study, a new two‐way relaying scheme based on compute‐and‐forward (CMF) framework and relay selection strategies is proposed, which provides a higher throughput than the conventional two‐way relaying schemes. Two cases of relays with or without feedback transmission capability are considered. An upper bound on the computation rate of each relay is derived, and based on that, a lower bound on the outage probability of the system is presented assuming block Rayleigh fading channels. Numerical results show that while the average sum rate of the system without feedback, named as max‐CMF (M‐CMF), reaches the derived upper bound only in low SNRs, that of the system with feedback, named as aligned‐CMF (A‐CMF) reaches the bound in all SNRs. However, both schemes approach the derived lower bound on the outage probability in all SNRs. For the A‐CMF, another power assignment …