Schisms constitute a common characteristic of human groups. Nevertheless, they have been neglected by social psychology, mainly because social psychological theories either dismiss group consensus or else depict groups as monolithic. This study proposes a social psychological approach to schism which integrates recent developments of self-categorization theory (SCT) with work on category argumentation. According to SCT, shared group identification leads to a process by which members should reach agreement. However, it is suggested that where members construe the positions of others as fundamentally altering group identity, then consensus is impossible. The corollary of assuming that groups will be consensual is that lack of consensus indicates the existence of different groups. This idea is examined through an analysis of a video and booklet produced for a rally organized by Forward in Faith, an organization opposed to the ordination of women as priests within the Church of England. It is shown that the existence of women priests is construed as changing the essence of the Church both on a structural level (by dividing it from the rest of the Christian community and turning it into a sect) and doctrinally. Such changes are seen as threatening the very existence of the Church of England and therefore demanding all out opposition. However, it is also shown that the decision of whether opponents fight the changes from inside the Church or by splitting from it depends upon the perception of whether they will be accorded the opportunity to advance their position from within. Thus schism is associated with both a perceived ‘change of essence’ and also with ‘lack of voice’.