  Let $(M^n,g)$ $(n\ge 4)$ be a complete noncompact $\kappa$-noncollapsed
steady Ricci soliton with $\rm{Rm}\geq 0$ and $\rm{Ric}> 0$ away from a compact
set $K$ of $M$.
  We prove that there is no any $(n-1)$-dimensional compact split limit Ricci
flow of type I arising from the blow-down of $(M, g)$, if there is an
$(n-1)$-dimensional noncompact split limit Ricci flow.
  Consequently, the compact split limit ancient flows of type I and type II
cannot occur simultaneously from the blow-down.
  As an application, we prove that $(M^n,g)$ with $\rm{Rm}\geq 0$ must be
isometric the Bryant Ricci soliton up to scaling, if there exists a sequence of
rescaled Ricci flows $(M,g_{p_i}(t); p_i)$ of $(M,g)$ converges subsequently to
a family of shrinking quotient cylinders.
