Using an operator method, a general description of waves (including the correct differential equations for the electromagnetic field) innonuniformmagnetized plasmas is given to all orders in electron and ion temperatures provided a few not too restrictive assumptions are made. This permits a correct differential treatment of a bounded plasma to a given order in temperature. When the plasma is uniform, this furnishes a useful temperature-ordered form of the corresponding dispersion equation. If the quasistatic approximation is made, we reobtain the Bernstein-type description of a plasma.