A　linear　transformation　is　proposed　to　deal　with　the　consensus　problem　of　high-order　linear　multi-agent　systems　(LMASs).　In　virtue　of　the　linear　transformation,　the　consensus　problem　is　equivalently　translated　into　a　partial　stability　problem.　We　discuss　three　issues　of　the　LMASs　under　a　generalized　linear　protocol:　1)　to　find　criteria　of　consensus　convergence;　2)　to　calculate　consensus　function;　3)　to　design　gain　matrices　in　the　linear　consensus　protocol.　Precisely,　we　provide　a　necessary　and　sufficient　criterion　of　consensus　convergence　in　terms　of　Hurwitz　stability　of　a　matrix　and　give　an　analytical　expression　of　the　consensus　function.　In　addition,　we　set　up　a　relation　between　the　gain　matrices　in　the　protocol　and　the　convergence　time　and　consensus　accuracy　of　the　agents,　and　then　design　the　gain　matrices　with　respect　to　a　pre-specified　convergence　time　and　a　required　consensus　accuracy.　©,　2014,　Acta　Automatica　Sinica.　All　rights　reserved.