This　paper　presents　a　Branch　and　Bound　method　for　a　nonconvex　integer　quadratic　programming　problem　with　a　separable　objective　function　over　a　bounded　box.　For　this　problem,　a　special　branch　method　is　constructed,　which　has　a　property　that　if　a　box　has　been　partitioned　into　2(n)　sub-boxes,　then　at　least　one　sub-box　can　be　deleted.　We　analyze　the　complexity　of　the　algorithm,　and　prove　that　it　is　better　than　that　of　the　complete　enumeration　method　in　the　worst　case　if　the　solution　space　is　large　enough.　(C)　2004　Elsevier　Inc.　All　rights　reserved.