In this paper a method to design tapered slot antenna (TSA), a member of ultra-wideband (UWB) antenna, is presented. The proposed method is related to impedance matching of input and free space intrinsic impedance by Butterworth method. By this method, curve fitting converts step impedance to optimized curve and this optimized curve and its symmetry create Vivaldi antenna. The fractional bandwidth (FBW) of the antenna by the proposed method is 155% which is more than the methods of Chebyshev and attenuation. A prototype of this antenna is fabricated and simulation and measurement results are in good agreement. Manuscript profile