This paper presents a method to remove correlated errors in GRACE (Gravity Recovery and Climate Experiment) data, which appear as long, linear features (stripes) in maps of surface mass variability. These stripes are caused by spatially correlated errors in the gravity field coefficients. The authors identify the spectral signature of these correlations and design a filter to remove them. The filter is applied to GRACE data and to a model of surface-mass variability to assess its effectiveness in preserving geophysical signals. GRACE data requires smoothing to reduce the effects of errors in short wavelength components. However, traditional smoothing methods do not account for correlated errors. The presence of stripes in unsmoothed data indicates that these errors are spatially correlated. The authors develop a filter that isolates and removes smoothly varying coefficients of like parity, which are responsible for the stripes. The filter is applied to GRACE data and to a model of surface-mass variability, showing that it effectively reduces stripes while preserving geophysical signals. The filter is derived by smoothing Stokes coefficients with a quadratic polynomial in a moving window. The resulting filter is then converted to a spatial representation. When applied to GRACE data, the filter reduces stripes and improves the signal-to-noise ratio in regions such as South America, Africa, and South Asia. When applied to a model of surface-mass variability, the filter reduces the amplitude of stripes while preserving geophysical signals. The filter is shown to be quite orthogonal to geophysical signals at these spatial scales. The authors conclude that the correlated-error filter effectively reduces the presence of stripes in GRACE data while preserving geophysical signals. They suggest that further research is needed to determine the source of these errors and incorporate them into the gravity field determination process. The filter provides a valuable tool for extracting more information from GRACE data.This paper presents a method to remove correlated errors in GRACE (Gravity Recovery and Climate Experiment) data, which appear as long, linear features (stripes) in maps of surface mass variability. These stripes are caused by spatially correlated errors in the gravity field coefficients. The authors identify the spectral signature of these correlations and design a filter to remove them. The filter is applied to GRACE data and to a model of surface-mass variability to assess its effectiveness in preserving geophysical signals. GRACE data requires smoothing to reduce the effects of errors in short wavelength components. However, traditional smoothing methods do not account for correlated errors. The presence of stripes in unsmoothed data indicates that these errors are spatially correlated. The authors develop a filter that isolates and removes smoothly varying coefficients of like parity, which are responsible for the stripes. The filter is applied to GRACE data and to a model of surface-mass variability, showing that it effectively reduces stripes while preserving geophysical signals. The filter is derived by smoothing Stokes coefficients with a quadratic polynomial in a moving window. The resulting filter is then converted to a spatial representation. When applied to GRACE data, the filter reduces stripes and improves the signal-to-noise ratio in regions such as South America, Africa, and South Asia. When applied to a model of surface-mass variability, the filter reduces the amplitude of stripes while preserving geophysical signals. The filter is shown to be quite orthogonal to geophysical signals at these spatial scales. The authors conclude that the correlated-error filter effectively reduces the presence of stripes in GRACE data while preserving geophysical signals. They suggest that further research is needed to determine the source of these errors and incorporate them into the gravity field determination process. The filter provides a valuable tool for extracting more information from GRACE data.