The object of preferred set selection is the identification of the minimum set of measurements that best characterizes a multicomponent system. The key set of rows (or columns) of a data matrix is the combination of rows (or columns) most orthogonal to each other. The key set optimizes data reproduction and therefore constitutes the preferred set. This paper describes an iterative refinement of the original key set methodology that ensures the selection of the most orthogonal set of typical vectors. Results of the iterative algorithm are compared with the noniterative procedure using a variety of data sets.