Exact　solutions　for　the　multidimensional　Schrodinger　map　equation　(SM　for　short)　on　hyperbolic　2-space　H-2　cone　are　obtained.　Consequently,　we　show　the　non-traveling　wave　solution　on　H-2　is　a　finite　energy　solution　on　the　finite　spacial　domain.　The　question　of　whether　a　solution　of　SM　can　develop　a　finite　time　singularity　on　H-2　with　smooth　initial　data　is　not　clear.　Our　result　show　that　blowup　can　really　happen　on　this　initial　data.　In　addition,　some　exact　global　smooth　solutions　are　constructed.