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Changes of the Pacific decadal oscillation (PDO) under global warming are investigated by using outputs from phase 5 of the Coupled Model Intercomparison Project (CMIP5) and a theoretical midlatitude air-sea coupled model. In a warming climate, the decadal variability of the PDO is found to be significantly suppressed, with the amplitude reduced and the decadal cycle shifted toward a higher-frequency band. We used the theoretical model put forward by Goodman and Marshall (herein the GM model) to underpin the potential mechanisms. The GM model exhibits a growing coupled mode that resembles the simulated PDO. It is found that the suppression of the PDO appears to be associated with the acceleration of Rossby waves due to the enhanced oceanic stratification under global warming. This shortens the PDO period and reduces PDO amplitude by limiting the growth time of the coupled mode. The GM model also suggests that the increase of growth rate due to strengthening of oceanic stratification tends to magnify the PDO amplitude, counteracting the Rossby wave effect. This growth rate influence, however, plays a secondary role.