Let Γ denote a bipartite Q-polynomial distance-regular graph with diameter d ⩾ 3 , valency k ⩾ 3 and intersection number c 2 = 1 . We show that Γ has a certain equitable partition of its vertex set which involves 4 d - 4 cells. We use this partition to show that the intersection numbers of Γ satisfy the following divisibility conditions: c i + 1 - 1 divides c i ( c i - 1 ) for 2 ⩽ i ⩽ d - 1 , b i - 1 - 1 divides b i ( b i - 1 ) for 1 ⩽ i ⩽ d - 1 . Using these divisibility conditions we show Γ does not exist if d = 4 .