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In this paper, we consider a two-way relay network (TWRN) employing amplify and forward (AF) relaying protocol and design a near optimal AF scheme to minimize the sum bit error rate (BER) of two end users. For the considered TWRN, in the first two time slots, each user respectively broadcasts its message to both the relay and the other user. Then, the relay linearly combines two received signals and broadcasts the combined signal to the two users. Closed-form near optimal combining coefficients at the relay are derived to minimize the sum BER of two users. Results show that the AF scheme with the proposed combining coefficients performs very closely to the scheme with optimal combining coefficients obtained by computer exhaustive search. It is also shown that the proposed AF scheme brings considerable gains to the system compared to the conventional AF with equal gain combining.