Summary: Aiming at normal criteria concerning derivative functions and shared meromorphic functions, the result is shown as follows. Let \(\Omega\) and \(a (z) (\ne 0)\) be a family of meromorphic functions and a meromorphic function in \(D\), respectively. If every \(\mu (z) \in \Omega\) satisfies conditions as follows: (1) \(\mu (z) \ne 0\), (2) for each of the same poles of \(\mu (z)\) and \(a (z)\), the multiplicities in \(\mu (z)\) are greater than or equal to the multiplicities in \(a (z)\), (3) for every function pair \(\{\mu (z), \nu (z)\} \subset \Omega\), \(\mu^{(m)} (z)\) and \(\nu^{(m)} (z)\) share \(a (z)\), then \(\Omega\) is normal in \(D\). Two examples are given to verify the necessity of conditions (1) and (2).