The diffuse component of solar radiation is an important, but understudied, component of the Earth's surface radiation budget. Most global climate models do not archive data on this component and observations of diffuse radiation are rare. Here, we archive a global 40-year (1980 - 2019) monthly radiation database called BaRAD (Bias-adjusted RADiation dataset) that includes the total shortwave radiation and its partitioning into its diffuse and direct beam components. The dataset is based on a random forest algorithm trained using the Global Energy Balance Archive (GEBA) monthly observation network and implemented on the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) dataset at the native MERRA-2 resolution (0.5 degree by 0.625 degree). The dataset picks up the seasonal, latitudinal, and long-term trends in the MERRA-2 data, but with reduced biases than MERRA-2.The dataset can reduce uncertainties in modelling surface energy and carbon budgets and help optimize the placement of concentrating solar power systems.