Abstract: In traditional principal component analysis (PCA), because of the neglect of the influence of dimensions on the system, the selected principal components (PCs) often fail to be representative. For this problem, an improved algorithm, called relative principal component analysis (RPCA), is proposed by introducing some new concepts, such as relative transform (RT), relative principal components (RPCs), "rotundity" scatter and so on. Firstly, the algorithm standardizes every variable's dimension in this system. Secondly, according to priori information, it analyzes and determines the different important levels of different variables. And then it allocates weights for each variable under the criterion of conservation of system energy. Finally, the algorithm utilizes the relative-principal-component model established to analyze system. Meanwhile, its functions are illustrated by some numerical examples such as data compression and system fault diagnosis. Both theoretic analysis and computer simulation have shown that these selected RPCs are representative and their significance of geometry is notable. So we can say that the new method may have extensive applications, together with the flexibility of PCs selection.