The site-preference rule (SPR), which is widely used to design and study the properties of full-Heusler alloys X2YZ, is applied to determine the positions of different transition-metal elements with various numbers of valence electrons in Heusler alloys. The scandium-based full Heusler alloys should form an XA structure according to the SPR, because the transition-metal element Sc with fewer valence electrons tends to occupy the Wyckoff sites A(0, 0, 0) and B(0.25, 0.25, 0.25). As opposed to previous investigations, L21-type scandium-based full Heusler alloys, which do not follow the SPR, are also considered in this work. Theoretical computations are used to study the atomic-site preferences of 171 scandium-based full Heusler alloys, and the results indicate that most of these alloys form L21-type structures rather than XA-type structures. Two possible orderings are also studied in terms of their difference in charge density. Furthermore, the ground state, electronic structure, and magnetic characteristics of these alloys are also investigated in detail in both XA and L21 structures. The results reveal dramatic differences between XA- and L21-type alloys. This study thus presents a counterexample of the SPR rule and should provide significant guidance for the future design of full-Heusler alloys.