An old method (often called graphical) for decomposing a mixed distribution to Gaussian components was generalized for the multidimensional case. The technique approximates an initial histogram by means of a sum of normally distributed components. A special separation algorithm for n-dimensional (nD) histograms was introduced for that purpose. Application of the separation method enables one to replace the customary pixel-by-pixel processing with a cluster-by-cluster procedure in any threshold algorithm. Stability of the algorithm was tested, comparing the decomposition of the radiation histograms produced by means of the Advanced Very High Resolution Radiometer (AVHRR) five channel measurements in the 3D and 5D cases for an area over Europe during nine orbits. The results show that multidimensional histograms are easily separable due to sufficiently large Euclidean distance between basic cloud and surface clusters in the measurement space. Applying the separation scheme in conjunction with a certain threshold technique to process the AVHRR-based histograms enables one to produce an automatic cloud detection algorithm. The algorithm sets necessary thresholds without auxiliary (i.e. beyond AVHRR) information and estimates average cloud amount, cloud top temperature and cloud reflectance at three levels for the histogram area. An example of such an algorithm for determining cloudiness parameters necessary for the Earth's radiation budget monitoring is presented.