||The general problem of computing posterior probabilities in Bayesian networds is NP-hard (Cooper 1990). However efficient algorithms are often possible for particular applications by exploiting problem structures. It is well understood that the key to the materialization of such a possibility is to make use of conditional independence and work with factorizations of joint probabilities rather than joint probabilities themselves. Differnent exact approaches can be characterized in terms of their choices of factorizations. We propose a new approach which adopts a straightforward way for factorizing joint probabilities. In comparison with the clique tree propagation approach, our approach is very simple. It allows the pruning of irrelevant variables, it accommodates changes to the knowledge base more easily. It is easier to implement. More importantly, it can be adapted to utilize both intercausal independence and conditional independence in one uniform framework. On the other hand, clique tree propagation is better in terms of facilitating pre-computations.