Word alignment is a critical procedure within statistical machine translation (SMT). Brown et al. (1993) have provided the most popular word alignment algorithm to date, one that has been implemented in the GIZA (Al-Onaizan et al., 1999) and GIZA++ (Och and Ney 2003) software and adopted by nearly every SMT project. In this article, we investigate whether this algorithm makes search errors when it computes Viterbi alignments, that is, whether it returns alignments that are sub-optimal according to a trained model.