In this paper we introduce a novel approach to manifold alignment, based on Procrustes analysis. Our approach differs from "semi-supervised alignment" in that it results in a mapping that is defined everywhere - when used with a suitable dimensionality reduction method - rather than just on the training data points. We describe and evaluate our approach both theoretically and experimentally, providing results showing useful knowledge transfer from one domain to another. Novel applications of our method including cross-lingual information retrieval and transfer learning in Markov decision processes are presented.