Variations in plasma density and magnetic field have a strong effect on the propagation of very low frequency waves in the whistler mode. Numerous studies have established that field‐aligned density irregularities (sometimes called ducts) symmetrical relative their axis can effectively guide whistlers along the ambient magnetic field. In this paper, we demonstrate that whistlers can be guided by a single transverse gradient in density when there is a gradient in the background magnetic field in the same direction as a density gradient. These gradients in the density and the background magnetic field forms two ducts: one on the inner edge of the density gradient and another on the outer edge. This situation is very relevant to what is observed in the Earth's magnetosphere near the plasmapause. Numerical simulations performed for the typical plasmapause densities and magnetic fields demonstrate trapping and propagation of whistler‐mode waves in these ducts.