This paper presents a new method for determining the site for power system stabilizer (PSS) installation. This method tracks the eigenvalues as they go from the interconnected power system to a decoupled system of single machine infinite buses (SMIB). The site for PSS installation is determined by observing to which machine the unstable eigenvalues from the interconnected system track to the decoupled system. This method is compared to the participation factor (PF) placement method for two different power system cases. The results show that the eigenvalue tracking and the PF placement method determined the same site for PSS installment in most cases. In the cases that they did not determine the same location, the eigenvalue tracking method determined the better site for PSS installment in a majority of cases. For completeness both the sites pointed out by the eigenvalue tracking method and the PF placement method should be investigated for PSS installment.