The　aim　of　this　paper　is　to　propose　a　simple　method　to　determine　the　number　of　distinct　eigenvalues　and　the　spectral　decomposition　of　covariance　matrix　for　a　variance　components　model.　The　method　introduced　in　this　paper　is　based　on　a　partial　ordering　of　symmetric　matrix　and　relation　matrix.　A　method　is　also　given　for　checking　straightforwardly　whether　these　distinct　eigenvalues　are　linear　dependent　as　functions　of　variance　components.　Some　examples　and　applications　to　illustrate　the　results　are　presented.　(C)　2006　Elsevier　Inc.　All　rights　reserved.