Consensus　analysis　and　design　problem　for　discrete-time　linear　multi-agent　systems　(DLMAS)　under　directed　information　topology　is　investigated.　A　proper　linear　transformation　is　proposed　to　transform　the　consensus　problem　to　the　partial　stability　problem　of　a　corresponding　linear　system.　Then,　a　new　consensus　criterion　in　terms　of　Schur　stability　of　matrices　for　DLMAS　achieving　consensus　under　directed　information　topologies　and　a　state　consensus　function　in　analytical　formulae　are　given.　Moreover,　a　design　process　to　determine　the　feedback　gain　matrix　in　the　consensus　protocol　is　proposed.　Numerical　examples　are　given　to　validate　the　above　theoretical　results.