  Cold collapse of a cluster composed of small identical clumps, each of which
is in virial equilibrium, is considered. Since the clumps have no relative
motion with respect to each other initially, the cluster collapses by its
gravity. At the first collapse of the cluster, most of the clumps are
destroyed, but some survive. In order to find the condition for the clumps to
survive, we made systematic study in two-parameter space: the number of the
clumps $N_c$ and the size of the clump $r_v$. We obtained the condition, $N_c
\gg 1$ and $n_k \geq 1$, where $n_k$ is related to $r_v$ and the initial radius
of the cluster $R_{ini}$ through the relation $R_{ini}/r_v = 2
N_c^{(n_k+5)/6}$. A simple analytic argument supports the numerical result.
This $n_k$ corresponds to the index of the power spectrum of the density
fluctuation in the cosmological hierarchical clustering, and thus our result
may suggest that in the systems smaller than $2/(\Omega h^2)$Mpc, the first
violent collapse is strong enough to sweep away all substructures which exist
before the collapse.
