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A new method for the flare's opening rate for a single radiator tapered slot antenna (TSA) is presented. A stepped quarter-wave Chebyshev transformer is calculated to minimize the frequency domain reflection and maximize the power transfer gain. Then slot widths are computed to match the Chebychev design, and smooth curves are fit to the computed steps. Different smoothing functions are compared, including the conventional exponential function, as well as cubic spline and Gaussian. The validity of the method is verified through simulations and measurements of experimental designs for the 1 to 3 GHz frequency range. In this work the TSA is fabricated on one side of a single layer Duroid substrate with dielectric constant 6.15. Although the Chebyshev transformer is an old concept, the novelty of this method is applying the transformer to design the TSA slotline taper profile, leading to a closed design procedure rather than an optimization. Advantages of this novel method are the straightforward mathematics of the design and that a simple simulation program can be written in a short time.