  The SOR-like iteration method for solving the absolute value equations~(AVE)
of finding a vector $x$ such that $Ax - |x| - b = 0$ with $\nu = \|A^{-1}\|_2 <
1$ is investigated. The convergence conditions of the SOR-like iteration method
proposed by Ke and Ma ([{\em Appl. Math. Comput.}, 311:195--202, 2017]) are
revisited and a new proof is given, which exhibits some insights in determining
the convergent region and the optimal iteration parameter. Along this line, the
optimal parameter which minimizes $\|T_\nu(\omega)\|_2$ with $$T_\nu(\omega) =
\left(\begin{array}{cc} |1-\omega| & \omega^2\nu \\ |1-\omega| & |1-\omega|
+\omega^2\nu \end{array}\right)$$ and the approximate optimal parameter which
minimizes $\eta_{\nu}(\omega) =\max\{|1-\omega|,\nu\omega^2\}$ are explored.
The optimal and approximate optimal parameters are iteration-independent and
the bigger value of $\nu$ is, the smaller convergent region of the iteration
parameter $\omega$ is. Numerical results are presented to demonstrate that the
SOR-like iteration method with the optimal parameter is superior to that with
the approximate optimal parameter proposed by Guo, Wu and Li ([{\em Appl. Math.
Lett.}, 97:107--113, 2019]). In some situation, the SOR-like itration method
with the optimal parameter performs better, in terms of CPU time, than the
generalized Newton method (Mangasarian, [{\em Optim. Lett.}, 3:101--108, 2009])
for solving the AVE.
