S. Baaj and G. Skandalis [C. R., Math., Acad. Sci. Paris 336, No. 4, 299–304 (2003; Zbl 1028.46083)] proved that every commutative multiplicative unitary on a separable Hilbert space is equivalent, up to tensoring with an \(n\)-dimensional Hilbert space, to the commutative multiplicative unitary induced from a certain locally compact group. In this paper, the author proves that it is possible to remove the condition on the separability of the Hilbert space provided that the commutative multiplicative unitary satisfies a regularity condition.