Part of understanding fictional narrative text is determining for each sentence whether it takes some character's point of view and, if it does, identifying the character whose point of view is taken. This paper presents part of an algorithm for perfomling the latter. When faced with a sentence that takes a character's point of view, the reader has to decide whether that character is a previously mentioned character or one mentioned in the sentence. We give particular consideration to sentences about private states, such as seeing and wanting, for which both possibilities exist. Our algorithm is based on regularities in the ways that texts initiate, continue, and resume a character's point of view, found during extensive examinations of published novels and short stories.