In this paper, the improvement of the cascaded prediction method was presented. The prediction method with backward adaptation and extended Ordinary Least Square (OLS+) was presented. An own approach to implementation of the effective context-dependent constant component removal block was used. Also the improved adaptive arithmetic coder with short, medium and long-term adaptation was used and the experiment was carried out comparing the results with other known lossless audio coders against which our method obtained the best efficiency.