A unitary matrix is any complex $N\times N$ matrix $U$ satisfying $UU^{\dagger}=\mathbb{1}_N$ where $\mathbb{1}_N$ is the identity matrix of dimension $N$. The symbol $\mathbb{U}(N)$ denotes the set of unitary matrices of dimension $N$.
Any rescaled Hadamard matrix $H/\sqrt{N}$ is unitary and all its elements have the same modulus.