Though the Atlantic multi-decadal oscillation (AMO) plays an important role in modulating regional and global climate, not only its definition is not universally agreed on for both observational and modeling studies, but also its governing mechanism is under intense debate. The challenge of defining the AMO in observations arises from that both natural/internal variability and forced climate response present in the observed record simultaneously. To separate the internal sea surface temperature (SST) variability from the externally forced changes in the North Atlantic, it becomes essential to remove the externally forced trend from the observations. By applying various strategies to isolate the forced response, we find that the resulting AMO index and its regional and global impacts heavily depend on how the externally forced trend is represented. A simple removal of the linear, global/local-mean SST trend will inevitably alias some forced responses into the resulting AMO since the temporal change of external forcing is not linear. The removal of global mean SST time series leads to a partial removal of the AMO’s influence on global or regional climate. Here, we propose that the best practice to define AMO is to remove the trend defined by the ensemble empirical mode decomposition that provides reasonable quadratic trends due to the anthropogenic radiative forcing. Although the temporal evolution of this AMO index is similar to the ones defined more traditionally, the cross-basin or global impacts of the AMO show distinct patterns, especially in the tropical Pacific.