Relational database systems suffer from the lack of a rich update language. In this paper we present the Update Dependency Language which allows the database designer to specify a procedure for each update that is activated when attempts are made to perform the update. Each procedure integrates the update dependencies for an update and provides an operational semantics for the update which is maintained by the system. We provide a formal definition for this language, illustrate its use, and discuss concurrency control issues related to integrating such a language into a database system.