We investigated and clarified the superstructures formed by tetrahedra in the bcc lattice within the framework of second-order transitions. Compliance with both the Landau and Lifshitz conditions was investigated for all possible superstructures and, based on this, we demonstrate that bcc crystals that contain tetrahedra at an inversion center can exhibit a variety of second-order transitions, which are regarded as a new type of diffusionless order-disorder transition with antiferroic orientational orders. Finally, we show that the transition gives rise to a new glassy state. Breaking of the local inversion symmetry may lead to a new orientational glass, which is reminiscent of spin glasses in magnetism.