It is proposed that the so-called 20-year wave in the diurnal variation of energetic cosmic rays is a consequence of the likely average odd symmetry of the interplanetary magnetic field about the solar equatorial plane. We assume that the magnetic field in each hemisphere of the solar magnetic cavity has the same average sense as the polar magnetic field at the corresponding solar pole. By considering the motion of energetic particles near the average plane of symmetry we find, with no further assumptions, that the direction, period, and phase of a 20-year wave in the diurnal anisotropy are implied. These implications agree with the observed variation of the diurnal anisotropy over a period of the full solar magnetic cycle. We give a simplified analytic computational model of the proposed mechanism and use it to calculate some further properties of the wave in a simple way. On the basis of this model we calculate the energy dependence of the anisotropy and find that it is in agreement with the observations.