Abstract We define a set of characters for the study of the fern family Gleicheniaceae. These characters have no ordered states. We establish a classification, through a divisive strategy, on the basis of these characters applied to the species occurring in the Greater Antilles. We used a technique based on information theory. A computational program was implemented to obtain this classification. With the same technique a procedure is used in order to compare a set of classifications reached under a different set of characters. The results obtained under three classifications on the family of this study are shown.