  We derive algebraic recurrence relations to obtain a deformation quantization
with separation of variables for a locally symmetric K\"ahler manifold. This
quantization method is one of the ways to perform a deformation quantization of
K\"ahler manifolds, which is introduced by Karabegov. From the recurrence
relations, concrete expressions of star products for one-dimensional local
symmetric K\"ahler manifolds and ${\mathbb C}P^N$ are constructed. The
recurrence relations for a Grassmann manifold $G_{2,2}$ are closely studied
too.
