In this paper, we consider multipoint-to-multipoint multi-input multi-output relay systems where multiple source-destination pairs simultaneously communicate through a single multiple antenna relay. In this system configuration, we minimize the maximum pairwise mean-squared-error (MSE) to guarantee fairness for all pairs. This problem is non-convex, and thus it is quite complex to find an analytical solution. In order to simplify this problem, we apply error covariance decomposition approach and broadcast channel to multiple access channel MSE duality, and then a pairwise MSE balancing scheme which utilizes global channel state information (CSI) is proposed. In order to reduce the complexity and CSI requirements, a new method is developed. Through numerical simulations, we confirm the effectiveness of our proposed schemes.