  We establish a closing property for thin trapped homoclinic classes. Taking
advantage of this property, we proved that if the homoclinic class $H(p)$
admits a dominated splitting $T_{H(p)}M=E\oplus_{<}F$, where $E$ is thin
trapped (see Definition \ref{Def:TP}) and all periodic points homoclinically
related to $p$ are uniformly $F$-expanding at the period (see Definition
\ref{Def:expanding}), then $F$ is expanded (see Definition \ref{Def:TP}).
