The multivariate reduced rank regression model plays an important role in econo- metrics. Examples include co-integration analysis and models with a factor struc- ture. Geweke (1996) provided the foundations for a Bayesian analysis of this model. Unfortunately several of the full conditional posterior distributions, which forms the basis for constructing a Gibbs sampler for the poster distribution, given by Geweke contains errors. This paper provides correct full conditional posteriors for the re- duced rank regression model under the prior distributions considered by Geweke.