  We investigate a particular aspect of the asymptotic expansion of the Wright
function ${}_1\Psi_1(z)$ for large $|z|$. The form of the exponentially small
expansion associated with this function on certain rays in the $z$-plane (known
as Stokes lines) is discussed. The main thrust of the paper is concerned with
the expansion in the particular case when the Stokes line coincides with the
negative real axis $\arg\,z=\pi$. Some numerical examples which confirm the
accuracy of the expansion are given.
