Regional mass fluxes owing to transport and adjustment within the Earth system that are implicitly contained in the monthly Gravity Recovery and Climate Experiment (GRACE) global geopotential coefficients are revealed by localizing global spectra using spatiospectrally concentrated window functions. We have analyzed 45 monthly global GRACE harmonic coefficient series in order to find the coseismic signature associated with the 2004 great Sumatra-Andaman earthquake. A significant gravity change after the earthquake is found in the time series of the GRACE coefficients after localization with a single band-limited window centered near the north of the island of Sumatra. This change is undetectable from the original global coefficients or from coefficients localized elsewhere on the globe. A step function with its discontinuity at 26 December 2004 usefully models the coseismic gravity change. The localized GRACE coefficients contain the jumps (associated with the earthquake) up to degree and order 55, although not all of them within this band produce changes that are statistically significant. The gravity change calculated from the localized GRACE coefficients displays 30 μGal peak-to-peak variations that are very well correlated with an independently derived seismic model based on elastic dislocation theory.