In many tasks associated with the large data sets processing, often arises a problem of compression with minimal loss of information in order to select the most essential features that define the nature of the phenomenon under investigation, data visualization, their transmitting over channels with limited bandwidth, etc. For solving such tasks principal component analysis (PCA) is widely used. This task is, also known as algebraic eigenvalue problem, or Karhunen-Loeve transformation. In situation when data sequentially are fed to processing in on-line mode, their volume is not known beforehand, and the system that generates the data is non-stationary, the traditional algorithms that implement the method of principal components loses its effectiveness and adaptive procedures based on neural network technology have to be used. In this regards, multistep self-learning rule for adaptive linear associator designed for finding eigenvalues and eigenvectors of the correlation matrix data that sequentially are fed to processing in on-line mode had proposed. This rule is a generalization of D. Hebb and E. Oja algorithms, used for neural networks training, implementing the method of principal components.