In a previous article, we used Hartree-Fock (HF) theory to study the piezoelectricity in BaTiO₃. In this paper, we applied the Douglas-Kroll-Hess second order scalar relativistic method to investigate the possible piezoelectric properties in the perovskite YFeO₃ structure, which has not yet been studied experimentally. The 30s20p13d and 31s21p17d Gaussian basis sets for the Fe (⁵D) and Y (²D) atoms, respectively, were built with the Generator Coordinate HF method. After contraction to [13s7p5d] and [13s8p7d], in combination with the 20s14p/6s4p basis set for the O (³P) atom from literature, they had their quality evaluated using calculations of the total and the orbital energies for the ²FeO⁺¹ and ¹YO⁺¹ fragments. The dipole moment, the total energy, and the total atomic charges in YFeO₃ in C(s) space group were calculated. The results and the analysis lead us to believe that the perovskite YFeO₃ does not present piezoelectric properties.