Alteration of the topological order by band inversion is a key ingredient of a topologically nontrivial material. Using first-principles calculations for HgTe, PtScBi, and Bi2Se3, we argue that it is not accurate to ascribe the band inversion to the spin-orbit coupling. Instead, scalar relativistic effects and/or lattice distortions are found to be essential. Therefore, the search for topologically nontrivial materials should focus on band shifts due to these mechanisms rather than spin-orbit coupling. We propose an effective scheme to search for new topological insulators.