For arbitrary wave propagation angle with respect to the magnetic field the wave cut-off and in particular, its dependence on the particle temperature are investigated. The obtained results demonstrate that when the wave propagation near the true cut-off (N = N = 0) as well as the cut-off of waves propagating at fixed, real N-value (N = 0, N0) are considered, it is essential to take relativistic effects into account. A simple expression is given for the cut-off density which is acceptable for most applications below T = 20 keV. In this temperature range it predicts values of the cut-off density of the ordinary mode which are close to the relativistic ones.