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Research activities to reduce the system complexity and energy consumption of digital relaying based cooperative wireless networks have yielded the demodulate-forward scheme where the relay performs demodulation, instead of decoding, on the received signals. On the other hand, cooperative maximum ratio combining (C-MRC) is another high-performance low-complexity technique used to combat error propagation in digital relaying without exploiting CRC codes which decreases the transmission efficiency. In this study, we propose a C-MRC based demodulate and forward protocol for two-way relay channels where two users exchange information via a relay. The transmission is divided into three phases in time where the first and second phases are allocated to the transmissions of uncoded or convolutionally encoded data of the users. After demodulation, the relay broadcasts the bit-wise XOR-ed packet to the users in the third phase. The numerical results for Rayleigh fading show that the proposed approach provides full diversity gain.