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As the High dynamic range (HDR) images generally have more than 10 bit/1024 colors per channel, its enormous data size often needs to be reduced when transmitting or storing the images. Thus development for functional compression is one of important research topics. Recently a lot of techniques for the HDR image compression are being suggested, and several two-layer coding algorithms which separately encode a low dynamic range (LDR) image and a residual image have been studied. However, those methods are inefficient in coding performance. In this article, we suggest a new two-layer coding algorithm for the HDR images, which realizes two-layered dynamic range. Our method encodes a base map, which is a blurred version of the HDR, and LDR image produced by the base map. Our algorithm significantly improves a compression performance.