Recent resting-state fMRI studies have revealed that the global signal (GS) exhibits a non-uniform spatial distribution across the gray matter. Whether this topography is informative remains largely unknown. We therefore tested rest-task modulation of global signal topography by analyzing static global signal correlation and dynamic co-activation patterns in a large sample of fMRI dataset (n=837) from the Human Connectome Project. The GS topography in the resting-state and in seven different tasks was first measured by correlating the global signal with the local timeseries (GSCORR). In the resting state, high GSCORR was observed mainly in the primary sensory and motor regions, while low GSCORR was seen in the association brain areas. This pattern changed during the seven tasks, with mainly decreased GSCORR in sensorimotor cortex. Importantly, this rest-task modulation of GSCORR could be traced to transient co-activation patterns at the peak period of global signal (GS-peak). By comparing the topography of GSCORR and respiration effects, we observed that the topography of respiration mimicked the topography of global signal in the resting-state whereas both differed during the task states; due to such partial dissociation, we assume that GSCORR could not be equated with a respiration effect. Finally, rest-task modulation of GS topography could not be exclusively explained by other sources of physiological noise. Together, we here demonstrate the informative nature of global signal topography by showing its rest-task modulation, the underlying dynamic co-activation patterns, and its partial dissociation from respiration effects during task states.