We have performed a reparameterization of PM6 (called rPM6) to compute open-shell species, specifically organic diradical molecules, within a framework of the spin-unrestricted semiempirical molecular orbital (SE-UMO) method. The parameters for the basic elements (hydrogen, carbon, nitrogen, and oxygen) have been optimized simultaneously using the training set consisting of 740 reference data. On the basis of the GMTKN30 database, the mean absolute error of rPM6 is decreased from 16.1 to 14.1 kcal/mol, which reassures its accuracy for ground-state properties. Applications of the spin-unrestricted rPM6 (UrPM6) method to small diradicals and relatively large polycyclic aromatic hydrocarbons have provided substantial improvement over the standard SE-UMO methods like UAM1, UPM3, and the original UPM6. The UrPM6 calculation is much less susceptible to spin contamination and, therefore, reproduces geometric parameters and adiabatic singlet-triplet energy gaps obtained by UDFT (UB3LYP and/or UBHandHLYP) at much lower computational cost.