Diagnostic keys are widely used in biology for the identification of specimens, but the technique is applicable to recognition processes in general. A key is constructed from a matrix which describes the properties of a set of objects. It is usually possible to contrive a large number of different keys for one set of objects, although the keys will not be equally useful. The construction and editing of keys by hand requires much labour, and a FORTRAN program is described here to do this automatically. The algorithm explores all the possible keys in a tree-searching process, and selects an optimal key heuristically. A special purpose data structure is used to represent the key in computer memory.