Abstract Elevation data are fundamental to many applications, especially in geosciences. The latest global elevation data contains forest and building artifacts that limit its usefulness for applications that require precise terrain heights, in particular flood simulation. Here, we use machine learning to remove buildings and forests from the Copernicus Digital Elevation Model to produce, for the first time, a global map of elevation with buildings and forests removed at 1 arc second (∼30 m) grid spacing. We train our correction algorithm on a unique set of reference elevation data from 12 countries, covering a wide range of climate zones and urban extents. Hence, this approach has much wider applicability compared to previous DEMs trained on data from a single country. Our method reduces mean absolute vertical error in built-up areas from 1.61 to 1.12 m, and in forests from 5.15 to 2.88 m. The new elevation map is more accurate than existing global elevation maps and will strengthen applications and models where high quality global terrain information is required.