  In this paper, we find the necessary and sufficient condition for the maximal
entanglement of the state, $ |\psi>=\mu|\alpha>|\beta>+\lambda|\alpha>|\delta>+
\rho|\gamma>|\beta>+\nu|\gamma>|\delta>,$ constructed by linearly independent
coherent states with \emph{real parameters} when
$<\alpha|\gamma>=<\beta|\delta>$. This is a further generalization of the
classified nonorthogonal states discussed in Ref. Physics Letters A {\bf{291}},
73-76 (2001).
