  For a meromorphic function $f$ in the unit disk $U=\{z:\;|z|<1\}$ and
arbitrary points $z_1,z_2$ in $U$ distinct from the poles of $f$, a sharp upper
bound on the product $|f'(z_1)f'(z_2)|$ is established. Further, we prove a
sharp distortion theorem involving the derivatives $f'(z_1)$, $f'(z_2)$ and the
Schwarzian derivatives $S_f(z_1)$, $S_f(z_2)$ for $z_1,z_2\in U$. Both
estimates hold true under some geometric restrictions on the image $f(U)$.
