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In this letter, we develop a novel, fast, nonlinear, and automated compound smoother, called RMMEH, to efficiently reduce noise of the normalized difference vegetation index (NDVI) time series and to reconstruct the MODIS NDVI time-series data with the two following main advantages: 1) ancillary data is not required, and 2) the whole procedure is automatically taken without any expert support. This new method involves several operations, including running medians smoother, arithmetic average, maximum (MAX) operation, and weighted moving average (WMA). The method is tested with the MODIS NDVI time series of MODIS/Terra Vegetation Indices 16-Day L3 Global 250m SIN Grid. Compared with other widely used smoothing techniques, this novel technique is proven to be more robust. It is simple in theory, easy to implement, efficient to operate, and resistant to most types of noise.