The (k, a) -generalized Fourier transform \( \mathscr {F}_{k, a} \) introduced by Ben Saïd–Kobayashi–Ørsted is a deformation family of the classical Fourier transform with a Dunkl parameter k and a parameter \( a > 0 \) that interpolates minimal representations of two different simple Lie groups. In the present paper, we focus on the case \( a < 0 \) . As a main result, we find a unitary transform that intertwines the known case \( a > 0 \) and the new case \( a < 0 \) .