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Two-way relaying has demonstrated significant gain in spectral efficiency by applying network coding when a pair of source nodes exchange information via a relay node. This paper is concerned with the scenario where multiple pairs of users exchange information through a common relay node equipped with multiple antennas. We aim to design linear precoding at the relay based on amplify-and-forward strategy. The goal is to maximize the minimum achievable rate among all the users subject to a peak relay power constraint so as to achieve the max-min fairness. We first convert this nonconvex problem into a series of semidefinite programming problems using bisection search and certain transformation techniques. A quasi-optimal solution is then obtained by using semidefinite relaxation (SDR). To reduce the design complexity, we further introduce a pair-wise zero-forcing (ZF) structure that eliminates the interference among different user pairs. By applying this structure, the precoding design problem is simplified to a power allocation problem which can be optimally solved. A simplified power allocation algorithm is also proposed. Simulation results show that the proposed SDR-based precoding not only achieves high minimum user rate but also maintains good sum-rate performance when compared with existing schemes. It is also shown that the proposed pair-wise ZF precoding with simplified power allocation strikes a good balance between performance and complexity.