Free decay of the non-dipole magnetic field is studied when the core is rotating relative to the conducting mantle. In the first place, the decay time for a stationary core is calculated, giving the time constants of 7300 years for the field n = 2 and 4400 years for n = 3. Secondly the effects of the weakly conducting mantle both on the decay constants and on the rotation of the fields are discussed. The results show, however, that these effects are negligibly small (less than 1%) when the conductivity of the lower mantle is assumed to be 10 −9 emu.