  We perform nonperturbative studies of the dimensionally reduced 5d
Yang-Mills-Chern-Simons model, in which a four-dimensional fuzzy manifold,
``fuzzy S$^{4}$'', is known to exist as a classical solution. Although the
action is unbounded from below, Monte Carlo simulations provide an evidence for
a well-defined vacuum, which stabilizes at large $N$, when the coefficient of
the Chern-Simons term is sufficiently small. The fuzzy S$^{4}$ prepared as an
initial configuration decays rapidly into this vacuum in the process of
thermalization. Thus we find that the model does not possess a ``fuzzy S$^{4}$
phase'' in contrast to our previous results on the fuzzy S$^{2}$.
