The shear in the magnetic field has been found to couple the resistive-g and ion temperature gradient instabilities to form a single, strongly growing mode. This result is first obtained from the structure of the turning points of these two instabilities and is confirmed by a numerical solution of the full radial eigenvalue problem. The dependence of the growth rate of this instability on shear, curvature, collisionality and ion temperature gradient is discussed – Comparisons are made between characteristics of this instability and the low-frequency fluctuations observed on the Culham Levitron.