In this paper we address the problem of how to extend the definition of functional dependencies (FDs) in incomplete relations to XML documents. An incomplete relation is said to strongly satisfy a FD if every completion of the relation, obtained by replacing all null values by data values, satisfies the FD in the ordinary sense. We propose a syntactic definition of strong FD satisfaction in a XML document (called a XFD) and then justify it by proving that for a very general class of mappings of a relation into a XML document, a relation strongly satisfies a unary FD if and only if the XML document also strongly satisfies the equivalent XFD.