A complex Hadamard matrix is called dephased if the entries of its first row and column are all equal to unity: $$\left[H\right]_{1,j}=\left[H\right]_{j,1}=1:j=1,2,...,N.$$ In case of real Hadamard matrices such a form is called normalised.
For any complex $N \times N$ Hadamard matrix $H$ there exist uniquely determined diagonal unitary matrices $$D_r={\rm diag}\left[{\bar H}_{11},{\bar H}_{21}, ..., {\bar H}_{N1}\right]$$ and $$D_c={\rm diag}\left[1,H_{11}{\bar H}_{12}, ..., H_{11}{\bar H}_{1N}\right]$$ such that matrix $H' = D_r H D_c$ is the dephased form of $H$. By definition, $H'$ is equivalent to $H$, $H'\simeq H$.