Summary: An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues \(\lambda_1\), \(\lambda_2,\dots,\lambda_r\) of the matrix satisfy \(|\lambda_1|\leqslant\cdots \leqslant|\lambda_r|\) and \(|\lambda_s| <|\lambda_{s+1}| (s\leqslant r-1)\), then associated with any eigenvalue \(\lambda_i(i\leqslant s)\), the errors of the eigenvalue and eigenvector derivatives obtained by the \(q\)th-order approximate method are proportional to \(|\lambda_i/\lambda_{s+1}|^{q+1}\), where the approximate method only uses the eigenpairs corresponding to \(\lambda_1\), \(\lambda_2,\dots,\lambda_s\). A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.