This paper presents and evaluates an original approach to automatically align bitexts at the word level. It relies on a syntactic dependency analysis of the source and target texts and is based on a machine-learning technique, namely inductive logic programming (ILP). We show that ILP is particularly well suited for this task in which the data can only be expressed by (translational and syntactic) relations. It allows us to infer easily rules called syntactic alignment rules. These rules make the most of the syntactic information to align words. A simple bootstrapping technique provides the examples needed by ILP, making this machine learning approach entirely automatic. Moreover, through different experiments, we show that this approach requires a very small amount of training data, and its performance rivals some of the best existing alignment systems. Furthermore, cases of syntactic isomorphisms or non-isomorphisms between the source language and the target language are easily identified through the inferred rules.