This　paper　investigates　the　decentralized　consensus　criteria　of　linear　multi-agent　systems　(MAS)　via　a　directed-spanning-tree-based　linear　transformation　method.　Firstly,　we　utilize　the　incidence　matrix　of　a　directed　spanning　tree　to　construct　a　linear　transformation　so　that　equivalently　transform　the　consensus　problem　into　a　stability　problem.　Secondly,　the　transformed　system　is　decomposed　into　a　decentralized　system　so　that　the　stability　criteria　can　be　obtained　in　a　decentralized　form.　Thus,　some　sufficient　criteria　for　the　MAS　in　decentralized　form　are　deduced.　Simulation　example　is　presented　to　verify　the　effectiveness　of　the　theoretical　results.　©　2019　IEEE.