When a parameterized dynamical system is not (structurally locally) identifiable, it is crucial to reparameterize the system to ensure that the new parameters can be uniquely determined, at least locally. In the article1, Theorem 2 claims the existence of an identifiable reparameterization for a parameterized analytic function under specified conditions. We first give a counter-example to show that its conditions are indeed incomplete. Next, to address its incompleteness, we will propose a modified version of the theorem.