To compute eigenvector derivatives with repeated eigenvalues, several extended Nelson's methods have been developed. Some of these methods have been pointed out that they may fail in some cases. To deal with those difficulties under repeated eigenvalues circumstances, we develop formulas to calculate sensitivities and discuss the case where repeated eigenvalues are present in this paper. The exact solution of derivatives of eigenvalue and eigenvector is presented by utilizing the mathematical theorem and new definitions of sensitivities. This algorithm is rigorous mathematically and suits for both distinct and multiple eigenvalues cases. The new technique is powerful, easy to implement and simple in its conception. For practical application, the probability is discussed to determining approximate solution by using lower order eigendata. Example will be presented that demonstrates the algorithm.