Let A be a d × d expansive matrix with |detA|=2. This paper addresses Parseval frame wavelets (PFWs) in the setting of reducing subspaces of . We prove that all semi‐orthogonal PFWs (semi‐orthogonal MRA PFWs) are precisely the ones with their dimension functions being non‐negative integer‐valued (0 or 1). We also characterize all MRA PFWs. Some examples are provided.
