This　paper　deals　with　the　output　consensus　problem　of　high-order　linear　multi-agent　systems.　A　generalized　linear　protocol　is　proposed,　which　consists　of　a　state　feedback　of　the　agent　itself　and　a　cooperative　protocol　in　a　generalized　feedback　form　of　the　relative　states　between　the　agents.　Then　a　state-linear-transformation　is　constructed　to　transform　the　output　consensus　problem　into　a　partial　stability　problem.　Based　on　the　partial　stability　theory,　a　necessary　and　sufficient　criterion　is　provided　for　the　linear　multi-agent　system　achieving　output　consensus,　which　is　expressed　in　terms　of　Hurwitz　stability　of　a　real　matrix　constructed　from　the　parameters　of　the　agent　models　and　the　protocol.