  This paper consists of tow parts. One is to study the existence of a point
$a$ in the intersection of Julia set and escaping set such that $\arg z=\theta$
is a singular direction if $\theta$ is a limit point of $\{\arg f^n(a)\}$ under
some growth condition of a meromorphic function. The other is to study the
connection between the Fatou set and singular direction. We prove that the
absent of singular direction deduces the non-existence of annuli in the Fatou
set.
