Well-known analytical results dealing with ion cyclotron and drift waves and which follow from the kinetic theory are used and the dispersion equation, which describes coupled two modes, is solved numerically. The numerical results obtained by using the values for the plasma density, magnetic field and temperature applicable to the solar corona clearly show the coupling and the instability (growing) of the two modes. The coupling happens at very short wavelengths, that are of the order of the ion gyro radius, and for characteristic scale lengths of the equilibrium density that are altitude dependent and may become of the order of only a few meters. The demonstrated instability of the two coupled modes (driven by the equilibrium density gradient) is obtained by using a rigorous kinetic theory model and for realistic parameter values. The physical mechanism which is behind the coupling is simple and is expected to take place throughout the solar atmosphere and the solar wind which contain a variety of very elongated density structures of various sizes. The mode grows on account of the density gradient, it is essentially an ion mode, and its further dissipation should result in an increased ion heating.