Different XML formats are widely used for data exchange and processing, being often necessary to mutually convert between them. Standard XML transformation languages, like XSLT or XQuery, are unsatisfactory for this purpose since they require writing a separate transformation for each direction. Existing bidirectional transformation languages mean to cover this gap, by allowing programmers to write a single program that denotes both transformations. However, they often 1) induce a more cumbersome programming style than their traditionally unidirectional relatives, to establish the link between source and target formats, and 2) offer limited configurability, by making implicit assumptions about how modifications to both formats should be translated that may not be easy to predict. This paper proposes a bidirectional XML update language called BiFluX (BIdirectional FunctionaL Updates for XML), inspired by the Flux XML update language. Our language adopts a novel bidirectional programming by update paradigm, where a program succinctly and precisely describes how to update a source document with a target document in an intuitive way, such that there is a unique “inverse” source query for each update program. BiFluX extends Flux with bidirectional actions that describe the connection between source and target formats. We introduce a core BiFluX language, and translate it into a formally verified bidirectional update language BiGUL to guarantee a BiFluX program is well-behaved.