  We study the special case of $n\times n$ 1D Gaussian Hermitian random band
matrices, when the covariance of the elements is determined by the matrix
$J=(-W^2\triangle+1)^{-1}$. Assuming that $n\ge CW\log W\gg 1$, we prove that
the averaged density of states coincides with the Wigner semicircle law up to
the correction of order $W^{-1}$.
