In a hot magnetized plasma large ion excursions can take place along the magnetic field lines, thereby introducing kinetic effects which cannot be treated in terms of a macroscopic fluid model. These effects are studied for transverse wave motions of ions and electrons in a homogeneous thermal plasma which is immersed in a homogeneous magnetic field. Strong kinetic wave damping is found to occur when the product kui of the wave number k and the ion thermal velocity ui exceeds the ion gyro frequency omega i. The physical mechanism of this damping originates from the ion excursions and differs from that of Landau and cyclotron damping. For plasmas having a comparatively low beta value, such as in Tokamak experiments, the present results indicate that kinetic damping becomes important only at small wave lengths, as compared to the dimensions of the plasma body. However, in high-beta systems, such as the Z-pinch, wave lengths in a large range become affected by kinetic damping, in some cases even those which are comparable to the characteristic macroscopic dimensions. This also affects the conditions of plasma stability and plasma high-frequency heating.