  We revise the structure-preserving finite element method in [K. Hu, Y. MA and
J. Xu. (2017) Stable finite element methods preserving $\nabla \cdot
\mathbf{B}=0$ exactly for MHD models. Numer. Math.,135, 371-396]. The revised
method is semi-implicit in time-discretization. We prove the linearized scheme
preserves the divergence free property for the magnetic field exactly at each
time step. Further, we showed the linearized scheme is unconditionally stable
and we obtain optimal convergence in the energy norm of the revised method even
for solutions with low regularity.
