  We study ground state properties of the $S=2$ quantum antiferromagnetic chain
with a uniaxially anisotropic Hamiltonian: $ H = \sum_{j} [S_{j} \cdot S_{j+1}
+ D (S^{z}_{j})^2 ] $ by a Monte Carlo calculation. While it has been reported
that a string order parameter vanishes exponentially at the isotropic
Heisenberg point ($D=0$), we found it tends to remain finite in the
thermodynamic limit around $D=1.2$. This implies that the model for $S=2$ has a
novel intermediate phase between the Haldane phase and the large-$D$ phase, as
was anticipated from the earlier argument based on the Valence-Bond-Solid
picture.
