A complex Hadamard matrix originally reported by K. Beauchamp and R. Nicoară as a single parameter family, which was then expanded to the three parameter one by P. Lampio et al. [19], reads; $$N_{10B}^{(3)}=\left[\begin{array}{rrrrrrrrrr} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\ 1 & 1 & -1 & -1 & 1 & 1 & -i & -1 & -1 & i\\ 1 & a & c & -ic & -a & -1 & -c & -i abc & i abc & ic\\ 1 & -a & -ic & c & a & -1 & -c & i abc & -i abc & ic\\ 1 & -i & -i a^{\ast}c & i a^{\ast}c & -1 & 1 & i & bc & -bc & -1\\ 1 & ib^{\ast} & -i a^{\ast}b^{\ast}c & i a^{\ast}b^{\ast}c & -ib^{\ast} & -1 & c & -c & ic & -ic\\ 1 & -ib^{\ast} & i a^{\ast}b^{\ast}c & -i a^{\ast}b^{\ast}c & ib^{\ast} & -1 & c & ic & -c & -ic\\ 1 & -1 & i a^{\ast}c & -i a^{\ast}c & -i & 1 & i & -bc & bc & -1\\ 1 & i & -c & -c & i & -i & -1 & c & c & -i\\ 1 & -1 & ic & ic & -1 & i & -i & -ic & -ic & 1 \end{array}\right],$$ where $a$, $b$ and $c$ are free phases and $^{\ast}$ is complex conjugate operator.