Monoclinic zirconia results from cubic -> tetragonal -> monoclinic phase transformations occurring at high temperature. Electron backscatter diffraction maps of monoclinic zirconia in fused-cast refractories have been treated with new crystallographic computer programs. The correct orientation relationships between the three phases have been identified among those proposed in the literature, the tetragonal and cubic parent grains have been automatically reconstructed, and the variants have been indexed. This example illustrates the possibilities of automatic crystallographic reconstruction software to study complex phase transition materials.