High dynamic range (HDR) images contain more details of the scene as compared to commonly used low dynamic range (LDR) images. The additional information in the HDR images is important for applications such as high-quality graphics rendering, sensing, scene analysis, and surveillance etc. Moreover, HDR images would provide better visualization experience on HDR displays, which might become more common in near future. Therefore, it is important to encode the entire dynamic range of the HDR images. In this paper, a new lossless, four-channel, eight bits per channel, format for encoding floating-point HDR images is proposed. The format is similar to the well-known RGBE format but constructs the E channel differently for better accuracy. Experimental results show that our technique could reduce the rounding error of the RGBE by more than 88%. In addition, there was a reduction of 44.3% in average error for all 33 images in the database used for this study.