The SPS kickers are major contributors to the SPS transverse beam coupling impedance. The current ”flat chamber” impedance model for a kicker is obtained by applying form factors to the theoretical impedance of an axisymmetric ferrite beam pipe. This model was believed to be acceptable for the vertical dipolar impedance, as twowire measurements on SPS kickers revealed a satisfactory agreement. However, one-wire measurements on PS kickers suggested that this model underestimates the kickers’ transverse quadrupolar (detuning) impedance. The longitudinal and transverse dipolar impedances of another kicker model that accounts for the metallic plates on each side of the ferrite were derived in the past by H. Tsutsui. The same formalism is used in this paper to derive the quadrupolar impedance. These formulae were then successfully benchmarked to electromagnetic (EM) simulations. Finally, simulating the interaction of an SPS bunch with the improved kickers’ model results in a positive horizontal tune shift, which is very close to the tune shift measured with the SPS beam.