Dynamic Bayesian networks （DBNs） can effectively perform modeling and qualitative reasoning for many dynamic systems. However, most of its inference algorithms involve complicated graphical transformations that are hard to program and time-consuming to compute. This article proposes a new recursive inference algorithm, which is a purely numerical method derived from probability theory and the characteristics of Bayesian networks to do both on-line and off-line inferences in discrete DBNs. The most prominent advantages of this novel approach include: （1） it is an exact inference algorithm, thus its accuracy and stability can be guaranteed, （2） it avoids the complex graphical transformation so as to remarkably improve the inference speed, and （3） its concise recursive formulae facilitate programming of both forwards and backwards pass. All of these issues are verified by accurate mathematical derivation as well as a couple of application examples with comparison between the new algorithm and the two most prevailing inference approaches of discrete DBNs - the interface algorithm and the forwards-backwards algorithm.
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