We　consider　a　class　of　linearly　constrained　separable　convex　programming　problems　whose　objective　functions　are　the　sum　of　m　convex　functions　without　coupled　variables.　The　alternating　proximal　gradient　method　is　an　effective　method　for　the　case　m　=　2,　but　it　is　unknown　whether　its　convergence　can　be　extended　to　the　general　case　m　＞=　3.　This　note　shows　the　global　convergence　of　this　extension　when　the　involved　functions　are　strongly　convex.　(c)　2013　Elsevier　Inc.　All　rights　reserved.