This　paper　studies　the　H-2　optimal　model　order　reduction　of　the　discrete　system　based　on　the　cross　Gramian,　which　equips　both　the　controllability　and　observability　information.　The　cross　Gramian　is　first　employed　to　obtain　the　H-2　norm　of　the　discrete　systems.　Then,　the　constrained　conditions　of　the　H-2　optimal　model　order　reduction　problem　of　the　discrete　systems　are　relaxed,　and　a　new　H-2　optimal　model　order　reduction　problem　on　the　product　manifold　is　reformulated.　Finally,　geometry　of　the　resultant　optimization　problem　is　investigated　and　an　iterative　algorithm　is　presented.　The　efficiency　of　the　proposed　algorithm　is　demonstrated　by　a　practical　example.　(C)　2019　Elsevier　Inc.　All　rights　reserved.