Fuzzy relational modelling is a ’grey-box’ method of modelling complicated, nan-linear systems directly from input-output data. Conventional methods of relational model identification, which rely on arguments based on set theory, are very fast, but do not produce models with very high accuracy. Identification using direct search numerical optimization is able to significantly increase model accuracy, but at the cost of greatly increased computation time. This paper describes a new method of fuzzy relational model identification which makes use of a particular form of relational model structure. The principal advantage of this structure is that it is linear in its parameters, allowing conventional linear least-squares techniques to be used to identify the model. The performance of the new technique is compared with previous methods of identification using the well established Box-Jenkins furnace data. The method is able to achieve very similar performance to the direct-search optimization methods, but in a fraction of the time. By embedding a model generated by the new technique in a model-based controller, and comparing the results with earlier work, it is also shown that the improved model accuracy greatly improves the controller performance.