Abstract Cross-lingual word embeddings (CLWE) underlie many multilingual natural language processing systems, often through orthogonal transformations of pre-trained monolingual embeddings. However, orthogonal mapping only works on language pairs whose embeddings are naturally isomorphic. For nonisomorphic pairs, our method (Iterative Normalization) transforms monolingual embeddings to make orthogonal alignment easier by simultaneously enforcing that (1) individual word vectors are unit length, and (2) each language’s average vector is zero. Iterative Normalization consistently improves word translation accuracy of three CLWE methods, with the largest improvement observed on EnglishJapanese (from 2% to 44% test accuracy)