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This paper describes a few basic characteristics of Ruedenberg bond order from both resonance-theoretic and molecular-orbital-theoretic aspect and manifests its usefulness and validity through illustrative bond order analysis of several regular alternants containing 4n-membered rings. Ruedenberg bond order is shown to be related with resonance structures exactly and to be regared as distributed valence which can be not only fractional but also negative or larger than unity in sharp contrast with Pauling bond order. It is pointed out that Ruedenberg bond order can reflect reactivity-stability characters of regular alternants more sensitively than Coulson bond order, having a close connection to the frontier orbital bond order. Behaviors of Ruedenberg and Pauling bond orders are compared in regular alternants containing 4n-membered rings and Pauling bond order is concluded to be a superfluous concept.