In this paper we present a novel steganography method for JPEG images. The proposed data hiding technique bases on removing and inserting AC coefficients 1 or -1. The candidates for removing and inserting are searched among all non rounded AC coefficients after quantization. The proposed search technique flags the most appropriate coefficients, which provide less degradation after modification. The proposed data hiding technique based on the modification the flagged coefficients significantly decreases distortion after data hiding and, as result, shows the less detectability for steganalysis. The proposed method was tested with steganalysis method proposed by T. Pevny and J.Fridrich. The experimental results show that the proposed method has less detectability compared to the existed widely used steganography methods as F5 and OutGuess.