We propose a method for making complex, self-assembling micromachined structures using two types of hinges that bend toward opposite directions, called "tani-ori" (valley-fold) and "yama-ori" (mountain-fold) in origami, the Japanese paper-folding technique. As an example, self-assembled microstages were fabricated. A multilayered structure including InGaAs strained layers was grown by molecular-beam epitaxy on a GaAs substrate. The top and bottom strained layers produce bending forces opposite to each other for "yama-ori" and "tani-ori," respectively. After releasing the multilayered structure from the substrate by the selective etching of a sacrificial layer, the microstage moved into its final position powered by the strain release in the InGaAs layers, where the stage was kept parallel to the substrate owing to the combination of the two types of hinges.