Synthetically useful aminodioximes are prepared via a novel three-component reaction among Z-chlorooximes, isocyanides, and hydroxylamines by exploiting the preferential attack of isocyanides to nitrile N-oxides via a [3 + 1] cycloaddition reaction. The results of quantum mechanical studies of the reaction mechanism are also discussed. Furthermore, the one-pot conversion of aminodioximes to 1,2,3-oxadiazole-5-amines via Mitsunobu-Beckmann rearrangement is reported for the first time.