Making use of the properties of eigenvalue and rank of matrices,the value of the determinant of the following Jacobian matrix is given: J=((∂yi)/(∂xj))n×n, yi=(xi)/(???19860314???xk2); i,j=1,2,...,n; extending the result in[1]to the case of n-dimensions This method is much simpler than that based on the fundamental properties of determinants.