  By the SYZ construction, a mirror pair $(X,\check{X})$ of a complex torus $X$
and a mirror partner $\check{X}$ of the complex torus $X$ is described as the
special Lagrangian torus fibrations $X \rightarrow B$ and $\check{X}
\rightarrow B$ on the same base space $B$. Then, by the SYZ transform, we can
construct a simple projectively flat bundle on $X$ from each affine Lagrangian
multi section of $\check{X} \rightarrow B$ with a unitary local system along
it. However, there are ambiguities of the choices of transition functions of
it, and this causes difficulties when we try to construct a functor between the
symplectic geometric category and the complex geometric category. In this
paper, we prove that there exists a bijection between the set of the
isomorphism classes of their objects by solving this problem.
