  Molecular dynamics simulations are performed for a supercooled simple liquid
with changing the system size from N=108 to $10^4$ to examine possible
finite-size effects. Although almost no systematic deviation is detected in the
static pair correlation functions, it is demonstrated that the structural
$\alpha$ relaxation in a small system becomes considerably slower than that in
larger systems for temperatures below $T_c$ at which the size of the
cooperative particle motions becomes comparable to the unit cell length of the
small system. The discrepancy increases with decreasing temperature.
