This paper presents a strategy for conducting Bayesian inference within the context of the triangular cointegration model. The numerical analysis is based on a hybrid of the Gibbs and Metropolis Markov Chain Monte Carlo methods. The use of a combination of two Markov Chain algorithms rather than a straight Gibbs Sampler occurs as a consequence of the complications induced by the prior specification. The specific form of the latter is, in turn, required for two purposes. First, in order to offset an identification problem which occurs when the cointegration model is extended to allow for the possibility of no cointegration. Second, in order to allow for an objective prior density on the parameter which determines the existence of cointegration.