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In this paper we consider a modified quasi-orthogonal space time type block code with optimum distance property for two-way (TW) wireless relay networks. This modified code is designed by using appropriate signal rotations and set partitioning of two quasi-orthogonal codebooks. The codebooks are formed from the union of two modified quasi-orthogonal codes, then the union is pruned down by one-half. A genetic algorithm (GA) is used to search for the optimum rotation matrix to maximize the distance property between the codes. In simulation studies the new code is shown to outperform previous open and closed loop distributed quasi-orthogonal space-time block coding (D-QO-STBC) schemes in terms of end-to-end codeword error rate, and thereby has potential application in wireless relays networks.