A multivariate spatial linear coregionalization model is considered that incorporates the Matérn class of covariograms. An EM algorithm is developed for maximum-likelihood estimation that has a few desirable properties and is capable of handling high-dimensional data. Most estimates in the EM algorithm are updated through closed form expressions and these estimates automatically satisfy necessary constraints. The model and algorithm are illustrated through a real example. Copyright © 2006 John Wiley & Sons, Ltd.