In order for the elements in the spectrum to represent different sequency components contained in the signal in a low-to-high order, we can re-order the rows (or columns) of the Hadamard matrix according to their sequencies.

The conversion of a given sequency into the corresponding index number in Hadamard order is a three-step process:

- represent in binary form:

- convert this binary form to Gray code:

where represents exclusive or and by definition. - bit-reverse 's to get 's:

where or equivalently .

For example,
, we have

Now the sequency-ordered or Walsh-ordered Walsh-Hadamard matrix can be obtained as

The first column on the right of the matrix is for the sequency of the corresponding row, which is the index for the sequency-ordered matrix, and the second column is the index of the Hadamard ordered. We see that this matrix is still symmetric: