  The electron reflection amplitude $R$ at stacking-fault (SF) induced
fractional steps is determined for Ag(111) surface states using a low
temperature scanning tunneling microscope. Unexpectedly, $R$ remains as high as
$0.6 \sim 0.8$ as energy increases from 0 to 0.5 eV, which is in clear contrast
to its rapidly decreasing behavior for monatomic (MA) steps [L. B{\"u}rgi et
al., Phys. Rev. Lett. \textbf{81}, 5370 (1998)]. Tight-binding calculations
based on {\em ab-initio} derived band structures confirm the experimental
finding. Furthermore, the phase shifts at descending SF steps are found to be
systematically larger than counterparts for ascending steps by $\approx 0.4
\pi$. These results indicate that the subsurface SF plane significantly
contributes to the reflection of surface states.
