We describe our study of II-VI alloy ZnSe0.5Te0.5 in search of spontaneous ordering. Samples were prepared by molecular beam epitaxy in a variety of structure configurations and growth temperatures, in order to scan a wide range of parameters and identify a favorable condition for ordering. Transmission electron microscopy was carried out on these samples and revealed indications of spontaneous ordering in several samples, where regions with stacking of atoms that appear to be different from the zinc-blende structure were observed. Preliminary study shows that such regions have the CuAu [i.e., the (100) superlattice] structure.