  In this paper we define a new transform on (generalized) Boolean functions,
which generalizes the Walsh-Hadamard, nega-Hadamard, $2^k$-Hadamard,
consta-Hadamard and all $HN$-transforms. We describe the behavior of what we
call the root- Hadamard transform for a generalized Boolean function $f$ in
terms of the binary components of $f$. Further, we define a notion of
complementarity (in the spirit of the Golay sequences) with respect to this
transform and furthermore, we describe the complementarity of a generalized
Boolean set with respect to the binary components of the elements of that set.
