In the paper, we present a new method for signal processing in statistical domain. The multiple components obtained from the conventional linear transformation are possibly irrelevant, and usually do not possess the characteristics of statistical independence. Therefore a method of signal decomposition and reconstruction is proposed based on the independent function element. This method not only inherits the advantages of linear transformation, but also has the capability of signal representation in the statistical domain. In this paper, the model, definition and obtaining method of independent function element are discussed, and the applications of heart sounds independent function element in the heart sound signal processing are also analyzed in detail. The validity and practicability of the method are demonstrated through two experiments.