  The HRT conjecture states that any finite collection of time-frequency shifts
of a non-zero square-integrable function on the real line is linearly
independent. In this paper, we establish the linear independence of finite
systems of time-frequency shifts of a non-zero meromorphic function.
Consequently, we prove that the conjecture is true for any square-integrable
function on $\mathbb{R}$ that can be extended to an analytic function on
$\mathbb{C}$ except on finitely many points.
