In this paper, the design and properties of a multi-fin coaxial waveguide converter are examined in detail. The converter has been designed as a means of transferring power from a high-power Relativistic Klystron Amplifier (RKA) to an antenna system. The output from an RKA is a coaxial waveguide, but the radially polarized TEM mode propagating in a coaxial line is not suitable for radiation. In order to transmit high electromagnetic (EM) power to the elements of a transmitting antenna, the polarization of the electric fields in the feeding waveguide should be parallel. A rectangular waveguide excited in the H1,0-mode has such a linear polarization. Therefore, it is necessary to provide a suitable matching transformer between the coaxial and rectangular waveguides. The purpose of the transformer is to convert the TEM mode in the coaxial line into the H1,0-mode in a number of rectangular waveguides. These are then connected to the antennas.