When　an　independent　estimate　of　covariance　matrix　is　available,　we　often　prefer　two-stage　estimate　(TSE).　Expressions　of　exact　covariance　matrix　of　the　TSE　obtained　by　using　all　and　some　covariables　in　covariance　adjustment　approach　are　given,　and　a　necessary　and　sufficient　condition　for　the　TSE　to　be　superior　to　the　least　square　estimate　and　related　large　sample　test　is　also　established.　Furthermore　the　TSE,　by　using　some　covariables,　is　expressed　as　weighted　least　square　estimate.　Basing　on　this　fact,　a　necessary　and　sufficient　condition　for　the　TSE　by　using　some　covariables　to　be　superior　to　the　TSE　by　using　all　covariables　is　obtained.　These　results　give　us　some　insight　into　the　selection　of　covariables　in　the　TSE　and　its　application.