The parametric decay of a whistler wave into a backscattered whistler wave and a forward scattered ion acoustic wave is investigated. The coupling coefficients for propagation parallel to a static magnetic field are derived in a homogeneous model, and applied to a model magnetosphere of the Earth by simulating gradients in the background plasma parameters in the direction of the magnetic field line with a set of damping coefficients. Computer model calculations are carried out for wave propagation inside the plasmapause along the field line L = 4 and it is shown that a minimum of the threshold field as expected appears in the equatorial region where the plasma is most homogeneous. The threshold field for a 10 kHz wave in the equatorial region is estimated to be ≅ 1 mV m-1, while the growth rate corresponding to this field strength is ≅ 4 Hz, which is an order of magnitude below the ion acoustic frequency. However, additional regions are found between the equatorial region and the ionosphere, where the gradients in the plasma parameters tend to match in such a way as to create regions of interaction with threshold fields of the same magnitude as those found in the equatorial region.