This note proposes a simple linear matrix inequality (LMI) system for the design of static precompensators to reduce the interactions of a multivariable system. The approach is based on minimizing the H-2 norm of a modified system and the LMIs are derived from the well known technique of pseudodiagonalisation. The approach is applied to two complex real-life benchmark problems with high levels of interaction. It is shown that its performance is significantly better than previously proposed LMI optimization techniques for designing static precompensators.