Intrinsic processes such as mesoscale turbulence have recently been proved as important as atmospheric variability in causing variations in ocean bottom pressure (pb). Intrinsic processes are also known to generate random variability on scales larger than the mesoscale through inverse energy cascades or large-scale baroclinic instability. Here, model analyses reveal a truly global-scale, intrinsic pb mode of variability at monthly time scales that relies on a different mechanism. The intrinsic mode has largest amplitudes around Drake Passage and opposite polarity between the Southern Ocean and Atlantic/Arctic oceans. Its signature is consistent with localized eddy-driven pb anomalies of opposite sign near Drake Passage that then adjust freely in the rest of the ocean via barotropic wave processes. This intrinsic mode seems consistent with observed pb variability.