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The commercial and military telecommunication systems require ultrawideband antennas. The small physical size and multi-band capability are very important in the design of ultrawideband antennas. Fractals have unique properties such as self-similarity and space-filling. The use of fractal geometry in antenna design provides a good method for achieving the desired miniaturization and multi-band properties. In this communication, a multi-band and broad-band microstrip antenna based on a new fractal geometry is presented. The proposed design is an octagonal fractal microstrip patch antenna. The simulation and optimization are performed using CST Microwave Studio simulator. The results show that the proposed microstrip antenna can be used for 10 GHz -50 GHz frequency range, i.e., it is a super wideband microstrip antenna with 40 GHz bandwidth. Radiation patterns and gains are also studied.