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Collocations are notoriously difficult for non-native speakers to translate, primarily because they are opaque and can not be translated on a word by word basis. We describe a program named Champollion which, given a pair of parallel corpora in two different languages, automatically produces translations of an input list of collocations. Our goal is to provide a tool to compile bilingual lexical information above the word level in multiple languages and domains. The algorithm we use is based on statistical methods and produces p word translations of n word collocations in which n and p need not be the same; the collocations can be either flexible or fixed compounds. For example, Champollion translates "to make a decision," "employment equity," and "stock market," respectively into: "prendre une decision," "équité en matière d'emploi," and "bourse." Testing and evaluation of Champollion on one year's worth of the Hansards corpus yielded 300 collocations and their translations, evaluated at 77% accuracy. In this paper, we describe the statistical measures used, the algorithm, and the implementation of Champollion, presenting our results and evaluation.