  We give a complex two-dimensional noncommutative locally symmetric K\"{a}hler
manifold via a deformation quantization with separation of variables. We
present an explicit formula of its star product by solving the system of
recurrence relations given by Hara-Sako. In the two-dimensional case, this
system of recurrence relations gives two types of equations corresponding to
the two coordinates. From the two types of recurrence relations, symmetrized
and antisymmetrized recurrence relations are obtained. The symmetrized one
gives the solution of the recurrence relation. From the antisymmetrized one,
the identities satisfied by the solution are obtained. The star products for
$\mathbb{C}^{2}$ and $\mathbb{C}P^{2}$ are constructed by the method obtained
in this study, and we verify that these star products satisfy the identities.
