For　the　mixed　effects　models　with　balanced　data,　a　new　ordering　of　design　matrices　of　random　effects　is　defined,　and　then　a　simple　formula　of　the　spectral　decomposition　of　covariance　matrix　is　obtained.　To　compare　with　the　two　methods　in　literature,　the　decomposition　can　not　only　give　the　actual　number　of　all　distinct　eigenvalues　and　their　expression,　but　also　show　clearly　the　relationship　between　the　design　matrices　of　random　effects　and　the　decomposition.　These　results　can　be　applied　to　the　problems　for　testifying　the　analysis　of　the　variance　estimate　being　a　minimum　variance　unbiased　under　all　random　effects　models　and　some　mixed　effects　models　with　balanced　data,　for　finding　the　explicit　solution　of　maximum　likelihood　equations　for　the　general　mixed　effects　model　and　for　showing　the　relationship　between　the　spectral　decomposition　estimate　and　the　analysis　of　variance　estimate.