This article presents the method Heliosat-2 that converts observations made by geostationary meteorological satellites into estimates of the global irradiation at ground level. This new version integrates the knowledge gained by various exploitations of the original method Heliosat and its varieties in a coherent and thorough way. It is based upon the same physical principles but the inputs to the method are calibrated radiances, instead of the digital counts output from the sensor. This change opens the possibilities of using known models of the physical processes in atmospheric optics, thus removing the need for empirically defined parameters and of pyranometric measurements to tune them. The ESRA models are used for modeling the clear-sky irradiation. The assessment of the ground albedo and the cloud albedo is based upon explicit formulations of the path radiance and the transmittance of the atmosphere. The method Heliosat-2 is applied to Meteosat images of Europe for the months of January 1995, April 1995 and July 1994. Pyranometric measurements performed by thirty-five meteorological stations are used to assess the performances that are close to those of Heliosat-1 found in the literature. Possible improvements are discussed.