Uncertainty is almost everywhere in the real world. Two existing models of approximate direction relations are direction relation matrices proposed by Cicerone and the 4-tuples model. Direction relation matrices are not proposed formally, and the decision method of their realizability does not always work well. On the other hand, the realizability decision method of the 4-tuples model is too complicated to be accomplished arithmetically. On these issues, DRMRB is proposed in this paper, then we present and certify the constraint rules of it; based on these rules, the constraint algorithm Realizability-Con () is implemented to obtain the realizable relations. Comparing with the two existing models, we find that DRMRB does not only have better results than the direction relation matrices; but it is also as expressive as the 4-tuples model and the decision algorithm of DRMRB is much simpler and easier to be achieved. © 2012 Binary Information Press.