  We study the impurity scattering on the $\pm$s-wave superconductor, with
realistic parameters for the Fe-pnictide superconductors. Using
$\mathcal{T}$-matrix method, generalized for the two bands, we found that
impurity scattering of the unitary limit forms off-centered bound states inside
of the superconducting gap, which modifies, surprisingly, the density of states
(DOS) of a fully opened gap to a V-shaped one as in the case of a d-wave
superconductor. This behavior provides coherent explanations to the several
conflicting experimental issues of the Fe-pnictide superconductors: the
V-shaped DOS but with an isotropic gap observed in the photoemission and
tunneling experiments; the power law behavior of the nuclear spin-lattice
relaxation rate ($1/T_1 \approx T^{\alpha}$ ; $\alpha \approx 3$), down to very
low temperatures.
