Abstract Inspired by the observation that word embeddings exhibit isomorphic structure across languages, we propose a novel method to induce a bilingual lexicon from only two sets of word embeddings, which are trained on monolingual source and target data respectively. This is achieved by formulating the task as point set registration which is a more general problem. We show that a transformation from the source to the target embedding space can be learned automatically without any form of cross-lingual supervision. By properly adapting a traditional point set registration model to make it be suitable for processing word embeddings, we achieved state-ofthe-art performance on the unsupervised bilingual lexicon induction task. The point set registration problem has been well-studied and can be solved by many elegant models, we thus opened up a new opportunity to capture the universal lexical semantic structure across languages