A family of complex Hadamard matrices $S_8^{(4)}(a,b,c,d)=S_8\circ{\rm EXP}\left(i R_{S_8^{(4)}}(a,b,c,d)\right)$, generated by the spectral matrix $S_8$, was found by M. Matolcsi et al. [34] in June 2006. We have $$S_8=\left[\begin{array}{rrrrrrrr} 1& 1& 1& 1& 1& 1& 1& 1\\ 1& 1& -1& -1& -1& i& -i& 1\\ 1& i& i& -i& 1& -1& -1& -i\\ 1& i& -i& i& -1& -i& i& -i\\ 1& -1& -i& i& 1& i& -i& -1\\ 1& -1& i& -i& -1& 1& 1& -1\\ 1& -i& -1& -1& 1& -i& i& i\\ 1& -i& 1& 1& -1& -1& -1& i\end{array}\right]$$ and $$R_{S_8^{(4)}}(a,b,c,d) = \left[\begin{array}{rrrrrrrr} \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet\\ \bullet& d& d& d& \bullet& c + d & c + d & d\\ \bullet& a - d & b - d & b - d & \bullet& \bullet& \bullet& a - d \\ \bullet& a& b& b& \bullet& c + d & c + d & a\\ \bullet& \bullet& b - d & b - d & \bullet& c& c& \bullet\\ \bullet& d& b& b& \bullet& d& d& d\\ \bullet& a - d & \bullet& \bullet& \bullet& c& c& a - d \\ \bullet& a& d& d& \bullet& d& d& a \end{array}\right].$$