Model Identification step plays an important and difficult part in time series analysis because the other steps of analysis depend on it and its accuracy. This article proposes an exact direct Bayesian technique to identify the order of bivariate autoregressive processes using Jeffreys' vague prior. Using the conditional likelihood function, the proposed technique is based on deriving the exact posterior probability mass function of the model order in a convenient form. Then one may easily evaluate the posterior probabilities of the model order and choose the order at which the posterior mass function attains its maximum to be the identified order. The performance of the proposed technique is checked using a P simulation study with three different prior mass functions. The analysis of the numerical results supports the adequacy of the proposed technique in identifying the orders of bivariate autoregressive processes.