Buhlmann(1944) established the validity of the block bootstrap proposed by Kunsch when it is applied to p-dimensional $alpha$-mixing dependent sequence. But his result requires a rather restrictive condition on p in the sense that p is entangled with dependence structure. We address that such restriction on p(or complication of dependence structure with p) could be removed completely when the underlying dependence structure is replace by more weakly dependent structure such as ø-mixing.