Hybrid screened density functional theory better describes the electronic structure of HgTe, CdTe, and HgCdTe systems in comparison with standard density functional theory. The newer hybrid functional reproduces the band inversion in the popular HgCdTe alloy justifying it as a better method than standard density functional theory in the search for new topological insulators. In addition, the 0.53 eV valence band offset obtained using the hybrid functional supports the recently observed higher band offset in the HgTe/CdTe heterostructure.