  Symbolic dynamics for homoclinic orbits in the two-dimensional symmetric map,
$x_{n+1}+cx_{n}+x_{n-1}=3x_{n}^3$, is discussed. Above a critical $c^{\ast}$,
the system exhibits a fully-developed horse-shoe so that its global behavior is
described by a complete ternary symbolic dynamics. The relative location of
homoclinic orbits is determined by their sequences according to a simple rule,
which can be used to numerically locate orbits in phase space. With the
decrease of $c$, more and more pairs of homoclinic orbits collide and
disappear. Forbidden zone in the symbolic space induced by the collision is
discussed.
