The problems of evaluating and subsequently maximizing the exact likelihood function of vector autoregressive moving average (ARMA) models are considered separately. A new and efficient procedure for evaluating the exact likelihood function is presented. This method puts together a set of useful features that can only be found separately in currently available algorithms. A procedure for maximizing the exact likelihood function, which takes full advantage of the properties offered by the evaluation algorithm, is also considered. Combining these two procedures, a new algorithm for exact maximum likelihood estimation of vector ARMA models is obtained. Comparisons with existing procedures, in terms of both analytical arguments and a numerical example, are given to show that the new estimation algorithm performs at least as well as existing ones, and that relevant real situations occur in which it does better.