  The effects of ambipolar diffusion on the linear stability of weakly ionised
accretion discs are examined. Earlier work on this topic has focused on axial
magnetic fields and perturbation wavenumbers. We consider here more general
field and wavenumber geometries, and find that qualitatively new results are
obtained. Provided a radial wavenumber and azimuthal field are present along
with their axial counterparts, ambipolar diffusion will always be
destabilising, with unstable local modes appearing at well-defined wavenumber
bands. The wavenumber corresponding to the maximum growth rate need not, in
general, lie along the vertical axis. Growth rates become small relative to the
local angular velocity when the ion-neutral collision time exceeds the orbital
time. In common with Hall electromotive forces, ambipolar diffusion
destabilises both positive and negative angular velocity gradients. In at least
some cases, therefore, uniformly rotating molecular cloud cores may reflect the
marginally stable state of the ambipolar magnetorotational instability.
