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.
