This　paper　presents　a　new　method　to　analyze　the　rotating　consensus　problem　of　linear　multi-agent　systems　(MASs).　First,　we　convert　the　rotating　consensus　problem　of　the　original　system　into　a　consensus　problem　of　corresponding　new　system　by　a　model　transformation,　and　also　introduce　the　consensus　protocol　of　the　original　system　to　achieve　consensus.　Then,　a　proper　linear　transformation　is　proposed　to　transform　the　consensus　problem　of　the　new　system　into　a　partial　stability　problem　of　corresponding　auxiliary　system.　Meanwhile,　we　design　the　gain　matrix　of　the　protocol　by　solving　a　bilinear　matrix　inequality　via　the　path-following　method.　Numerical　examples　of　directed　and　undirected　information　topologies　are　given　to　illustrate　the　effectiveness　of　the　theoretical　results.