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In this paper, we present a new window function for design of FIR filters using IIR filters which has superior performance compared to the previously presented windows. The new window has approximately the same main lobe width as that of the Blackman window, while featuring about 9-11 dB smaller side lobe peak. The idea behind the design of the proposed window is to use the extended Kalman filtering. Our results also show substantial performance improvement of the proposed window compared to the Gaussian, Kaiser, and Lanczos windows. An application example, design of FIR low pass filter by windowing method, verifies the efficiency of the new window.