  In this paper, we study the uniqueness of the direct decomposition of a toric
manifold. We first observe that the direct decomposition of a toric manifold as
\emph{algebraic varieties} is unique up to order of the factors. An
algebraically indecomposable toric manifold happens to decompose as smooth
manifold and no criterion is known for two toric manifolds to be diffeomorphic,
so the unique decomposition problem for toric manifolds as \emph{smooth
manifolds} is highly nontrivial and nothing seems known for the problem so far.
We prove that this problem is affirmative if the complex dimension of each
factor in the decomposition is less than or equal to two. A similar argument
shows that the direct decomposition of a smooth manifold into copies of
$\mathbb{C}P^1$ and simply connected closed smooth 4-manifolds with smooth
actions of $(S^1)^2$ is unique up to order of the factors.
