This paper describes an efficient lossless coding method for HDR color images stored in a floating point format called radiance RGBE. In this method, three mantissa parts of RGB components as well as a common exponent part, each of which is represented in 8-bit depth, are encoded by the block-adaptive prediction technique. In order to improve the prediction accuracy, mantissa parts of RGB components used in the prediction are adjusted so that their exponent parts can be regarded as same. Moreover, not only the same color but also already encoded other color components are used in the prediction to exploit inter-color correlations. Simulation results indicate that introduction of the above exponent equalization as well as inter-color prediction can considerably improve the coding efficiency.