We address the behavior of the Dirac equation with scalar (S), vector (V), and tensor (U) interactions under the γ5 discrete chiral transformation. By using this transformation, in a simple way, we can obtain solutions for the Dirac equation with spin (Δ=VS=0) and pseudospin (Σ=V+S=0) symmetries, which includes a tensor interaction. As an application, the Dirac equation with scalar, vector, and tensor Cornell radial potentials is considered, and the correct solution to this problem is obtained. © 2012 American Physical Society.