  In \cite{btoric}, Guillemin et al. proved a Delzant-type theorem which
classifies $b$-symplectic toric manifolds. More generally, in \cite{torus} they
proved a similar convexity result for general Hamiltonian torus action on
$b$-symplectic manifolds. In this paper, we provide a new way to construct
$b$-symplectic toric manifolds from usual toric manifolds. Conversely, through
this way, we can also decompose a $b$-symplectic toric manifolds to usual toric
manifolds. Finally, we will try to prove that this kind of decomposition is
useful, although the symplectic structure for our decomposition or construction
is not canonical.
