Generalised Procrustes Analysis (GPA) is a method for matching several, possibly large, data sets by fitting them to each other using transformations, typically rotations. The linear version of GPA has been applied in a wide range of contexts. A non-linear extension of GPA is developed which uses Optimal Scaling (OS). The approach is suited to match data sets that contain nominal variables. A database of a Dutch power supplier that contains many categorical variables unfit for the usual linear GPA methodology is used to illustrate the approach.