  The twist interval of a twist map on the annulus $A=\mathbb{T}\times [0,1]$
has nonempty interior if $f$ preserves the area, but could be degenerate for
general twist maps. In this note, we show that if a twist map $f$ is
non-wandering, then the twist interval of $f$ is non-degenerate. Moreover, if
there are two disjoint invariant curves of $f$, then their rotation numbers
must be different (no matter if they are rational or irrational).
