  It is known that there are three maximally entangled states $\ket{\Phi_1} =
(\ket{0000} + \ket{1111}) / \sqrt{2}$, $\ket{\Phi_2} = (\sqrt{2} \ket{1111} +
\ket{1000} + \ket{0100} + \ket{0010} + \ket{0001}) / \sqrt{6}$, and
$\ket{\Phi_3} = (\ket{1111} + \ket{1100} + \ket{0010} + \ket{0001}) / 2$ in
four-qubit system. It is also known that there are three independent measures
${\cal F}^{(4)}_j \hspace{.2cm} (j=1,2,3)$ for true four-way quantum
entanglement in the same system. In this paper we compute ${\cal F}^{(4)}_j$
and their corresponding linear monotones ${\cal G}^{(4)}_j$ for three rank-two
mixed states $\rho_j = p \ket{\Phi_j}\bra{\Phi_j} + (1 - p) \ket{\mbox{W}_4}
\bra{\mbox{W}_4}$, where $\ket{\mbox{W}_4} = (\ket{0111} + \ket{1011} +
\ket{1101} + \ket{1110}) / 2$. We discuss the possible applications of our
results briefly.
