In　this　paper,　the　problem　of　estimating　the　covariance　matrix　in　general　linear　mixed　models　is　considered.　A　new　class　of　estimators　is　proposed.　It　is　shown　that　this　new　estimator　dominates　the　analysis　of　variance　estimate　under　two　squared　loss　functions.　Finally,　some　simulation　results　to　compare　the　performance　of　the　proposed　estimator　with　that　of　the　analysis　of　variance　estimate　are　reported.　The　simulation　results　indicate　that　this　new　estimator　provides　a　substantial　improvement　in　risk　under　most　situations.