Let　T-1,　T-2,...,T-k　be　spanning　trees　of　a　graph　G.　For　any　two　vertices　u,　v　of　G,　if　the　paths　from　u　to　v　in　these　k　trees　are　pairwise　openly　disjoint,　then　we　say　that　T-1,　T-2,...,T-k　are　completely　independent.　Araki　showed　that　a　graph　G　on　n　＞=　7　vertices　has　two　completely　independent　spanning　trees　if　the　minimum　degree　delta(G)　＞=　n/2.　In　this　paper,　we　give　a　generalization:　a　graph　G　on　n　＞=　4k　-　1　vertices　has　k　completely　independent　spanning　trees　if　the　minimum　degree　delta(G)　＞=　k-1/kn.　In　fact,　we　prove　a　stronger　result.　(C)　2016　Elsevier　B.V.　All　rights　reserved.