Schisms within groups are extremely widespread, yet the phenomenon has been virtually ignored within social psychology. Indeed prominent theories of group process virtually exclude the possibility of schism by presupposing the unitary nature of group identity. In this paper we offer a social psychological approach to the schismatic process based on the idea that, while group members may expect to achieve consensus, the issue of where that consensus should reside may be a matter of argument. When differing constructions cannot be reconciled such that what one faction considers to represent group identity is seen by the another to contradict group identity, then the basis for schism exists. This approach is illustrated using an analysis of the 1991 split of the Italian Communist Party (PCI) into two organizations, the PDS and RC. Interviews with 26 members of these two organizations show that they produce different arguments concerning the identity of the categories involved. However, all the arguments are structured so as to construe the ingroup faction as consonant with the true identity of the PCI and the outgroup faction as dissonant with that identity. The implication of this analysis both for a social psychology of schism and for the conceptualization of group consensus are discussed. © 1998 John Wiley & Sons, Ltd.