Fast calculation of the Hadamard transform of a 4X4 matrix

Question

I'm reading a book envolves Hadamard transformations, and in one of the examples they are trying to reconstruct Y from RX+Z where all are 4X4 matrixes.
R is given by:
R= 1/4 * \begin{array}{l}5&3&3&-3\\3&5&-3&3\\3&-3&5&3\\-3&3&3&5\end{array} And one step further (without any explanation they write that
H(R) = HRH =
\begin{array}{l}2&0&0&0\\0&2&0&0\\0&0&2&0\\0&0&0&-1\end{array}
Did they calculate HRH "behind the scenes" or there's a fast way of calculating the transform gives certain characteristics to the matrix?