MATCH matches up items in two different lists, which can have two different systems of coordinates. The program allows the two sets of coordinates to be related by a linear, quadratic, or cubic transformation. MATCH was designed and written to work on lists of stars and other astronomical objects but can be applied to other types of data. In order to match two lists of N points, the main algorithm calls for O(N^6) operations; though not the most efficient choice, it does allow for arbitrary translation, rotation, and scaling.