One of the necessary extensions to the centering model is a mechanism to handle pronouns with intrasentential antecedents. Existing centering models deal only with discourses consisting of simple sentences. It leaves unclear how to delimit center-updating utterance units and how to process complex utterances consisting of multiple clauses. In this paper, I will explore the extent to which a straightforward extension of an existing intersentential centering model contributes to this effect. I will motivate an approach that breaks a complex sentence into a hierarchy of center-updating units and proposes the preferred interpretation of a pronoun in its local context arbitrarily deep in the given sentence structure. This approach will be substantiated with examples from naturally occurring written discourses.