Abstract: Let G be a graph, if there exists a partition { V1 ,V2 , ?,Vn } ofV (G) satisfying G[Vi ] a multip le comp lete bigraph for any i (1≤i≤n) , then G has a CB2partition. Combined with the condition of CB2partition, it gives classes of upper - embeddable graphs whose value of degree of each vertex is 0, 1 or 3 respectively, under module 4. Based on the known results, it characterizes entirely the upper embeddablity of such classes of graphs.