This　paper　proposes　a　decentralized　design　approach　of　consensus　protocols　of　multi-agent　systems　(MASs)　via　a　directed-spanning-tree(DST)-based　linear　transformation　and　the　corresponding　minimal　communication　links.　First,　the　consensus　problem　of　multi-agent　systems　is　transformed　into　the　decentralized　output　stabilization　problem　by　constructing　a　linear　transformation　based　on　a　DST　of　the　communication　topology,　and　thus　a　necessary　and　sufficient　consensus　criterion　in　terms　of　decentralized　fixed　mode　(DFM)　is　derived.　Next,　a　new　distributed　protocol　is　designed　by　using　only　the　neighbors＇　information　on　the　DST,　which　is　a　fully　decentralized　design　approach.　Finally,　some　numerical　examples　are　given　to　verify　the　results　attained.　©　2023　IEEE.