  The blow up phenomenon in the first step of the classical Picard's scheme was
proved in this paper. For certain initial spaces, Bourgain-Pavlovi\'c and
Yoneda proved the ill-posedness of the Navier-Stokes equations by showing the
norm inflation in certain solution spaces. But Chemin and Gallagher said the
space $\dot{B}^{-1,\infty}_{\infty}$ seems to be optimal for some solution
spaces best chosen. In this paper, we consider more general initial spaces than
Bourgain-Pavlovi\'c and Yoneda did and establish ill-posedness result
independent of the choice of solution space. Our result is a complement of the
previous ill-posedness results on Navier-Stokes equations.
