The problem of synthesizing a film attenuator made by applying an absorbing material to a conductor is considered. Since the absorbing material has a parameter of maximum dissipated power per unit area, then when synthesizing an attenuator to attenuate high powers, the problem of exceeding the maximum dissipated power per unit area may arise. A sectional attenuator structure has been proposed, which is a set of sections having different attenuation to reduce the power dissipated per unit area. An algorithm for the synthesis of a sectional attenuator is proposed. The attenuator sections are rectangles of various widths. The attenuation distribution is performed using the Taylor series expansion of mathematical functions. The properties of the functions used to distribute the attenuation related to the problem under consideration were considered. The graphs of the dependence of power on the attenuator section are presented. Power distribution has been confirmed by simulation results. Theoretical calculations were confirmed by simulation results in the CST Microwave Studio software.