This paper deals with the decentralized hierarchical PSS (Power System Stabilizer) controller design to achieve a better damping of specific inter-area oscillations. The two-level decentralized hierarchical structure consists of two PSS controllers. The first level controller is a local PSS controller for each generator to damp local mode in the area where controller is located. This controller uses only local signals as input signals. The local signal comes from the generator at which the controller is located. The secondary level controller is a multivariable decentralized global PSS controller to damp inter-area modes. This controller uses selected suitable wide area PMU (Phasor Measurement Units) signals as inputs. The PMU or global signals are taken from network locations where the oscillations are well observable. The global controller uses only those global input signals in which the assigned single inter-area mode is most observable and is located at a generator that is most effective in controlling the assigned mode. The global controller works mainly in a frequency band given by the natural frequency of the assigned mode. The effectiveness of the resulting hierarchical controller is demonstrated through simulation studies conducted on a test power system.