When two alternative treatments (A and B) are available, some subgroup of patients may display a better outcome with treatment A than with B, whereas for another subgroup, the reverse may be true. If this is the case, a qualitative (i.e., disordinal) treatment–subgroup interaction is present. Such interactions imply that some subgroups of patients should be treated differently and are therefore most relevant for personalized medicine. In case of data from randomized clinical trials with many patient characteristics that could interact with treatment in a complex way, a suitable statistical approach to detect qualitative treatment–subgroup interactions is not yet available. As a way out, in the present paper, we propose a new method for this purpose, called QUalitative INteraction Trees (QUINT). QUINT results in a binary tree that subdivides the patients into terminal nodes on the basis of patient characteristics; these nodes are further assigned to one of three classes: a first for which A is better than B, a second for which B is better than A, and an optional third for which type of treatment makes no difference. Results of QUINT on simulated data showed satisfactory performance, with regard to optimization and recovery. Results of an application to real data suggested that, compared with other approaches, QUINT provided a more pronounced picture of the qualitative interactions that are present in the data. Copyright © 2013 John Wiley & Sons, Ltd.