This paper addresses a novel steganography method for images. Most statistical steganalysis algorithms are strong to defeat previous steganography algorithms. RS steganalysis and pixel difference histogram analysis are two well-known statistical steganalysis algorithms which detect non-random changes caused by embedding a secret message into cover image. In this paper, we first explain how two steganalysis algorithms exploit the effect of the non-random changes and then propose a new steganography method that avoids the non-random changes to evade statistical analysis methods. For this purpose, we adjust the embedding process to be more adaptive to cover image by considering embedding in Gray code bit planes, not natural binary bit planes, of cover images, and two parameters: (1) similarity threshold for selecting non-flat area in lower bit planes, and (2) size of flat blocks
in embedding bit planes. Experimental results show that the secret messages embedded by our method are undetectable under RS steganalysis and pixel difference histogram analysis.