Abstract: A simplified method is presedted for the determination of the first-and second-order and higher order derivatives of eigenvetorys. In the procedure, by using the normaligation condition of eigenvctors, the matrix of the original eigensystem of rank （n- 1 ） is modified directly to be a matrix of rank n. Then the derivatives of eigenvectors are solved directly by using LU decomposition-bank-substitution method. Examples show that the calculated results of the present method are the same as that of Nelson's method. However, this method is more concise in conception and simpler than Nelson's method. In addition, the second, and higher order derivatives of the eigenvectors can also be solved.