  We investigate stability of a gravitationally collapsing iron core against
non-spherical perturbation. The gravitationally collapsing iron core is
approximated by a similarity solution for dynamically collapsing polytropic gas
sphere. We find that the similarity solution is unstable against non-spherical
perturbations. The perturbation grows in proportion to $ (t - t_0) ^{-\sigma} $
while the the central density increases in proportion to $ (t - t_0) ^{-2} $.
The growth rate is $ \sigma = 1/3 + \ell (\gamma - 4/3) $, where $ \gamma $ and
$ \ell $ denote the polytropic index and the parameter $ \ell $ of the
spherical harmonics, $ Y_{\ell} ^m (\theta, \phi) $, respectively. The growing
perturbation is dominated by vortex motion. Thus it excites global convection
during the collapse and may contribute to material mixing in a type II
supernova.
