Many multivariable (systems with many inputs/outputs) industrial processes can, to a good degree of approximation, be modelled by a transfer function matrix, where all of the interaction occurs in a matrix of constant coefficients. This reflects the fact that the dynamics of the section in which the interaction occurs are very fast compared with the other dynamics in the system. Examples of such systems include steel rolling mills and boiler systems. Such multivariable systems are relatively easy to design controllers for, since the system may be diagonalised by an inverse of the constant gain matrix, followed by suitable single-loop dynamic compensation. However, this approach depends on the linearity of the dynamical elements in the system. Such a condition is voilated by the presence of non-linear actuators, which are a feature of many industrial systems. The presence of such actuators within a multivariable control system as described above can cause very significant interaction problems, with associated degradation in performance, particularly during transients. This paper describes a straightforward technique, which is effective in linearising typical non-linear industrial actuators, allowing diagonalisation to be effectively achieved at all frequencies. The technique relies on a simple describing function analysis and manifests itself as a time-varying linearising precompensator for each non-linear actuator. A simple example is used to demonstrate the effectiveness of the method and it is then shown in application with multivariable boiler and steel mill models.