  Let $\mathfrak{A}$ and $\mathfrak{A}'$ be two $C^*$-algebras with identities
$I_{\mathfrak{A}}$ and $I_{\mathfrak{A}'}$, respectively, and $P_1$ and $P_2 =
I_{\mathfrak{A}} - P_1$ nontrivial symmetric projections in $\mathfrak{A}$. In
this paper we study the characterization of multiplicative $*$-Lie-type maps.
In particular, if $\mathcal{M}$ is a factor von Neumann algebra then every
complex scalar multiplication bijective unital multiplicative $*$-Lie-type map
is $*$-isomorphism.
