Normal matrix that isn't unitary

Question

Can anyone give me an example of a normal matrix that isn't unitary? Here, $A \in \mathbb{C^{n \times n}}$.

Answer 1

Take every $A$ with $A=A^{H}$ where $H$ denotes the Hermitian transform(conjugate transposed). For example $A=\begin{pmatrix} 4 & 2i\\-2i & 4 \end{pmatrix}$