The performance of a novel taper slot antenna (TSA) with a tapered profile that conforms to a fourth order polynomial function is reported. This polynomial tapered profile has a larger opening rate at higher frequency than the conventional Vivaldi flare. A short 0.5λ long polynomial flared TSA was modelled and its computed properties compared with those of a Vivaldi of similar length. The polynomial TSA showed a higher boresight gain, better matching characteristics and similar levels of cross-polarisation isolation over the design bandwidth of 6-18 GHz. A prototype polynomial TSA was constructed and measurements of input impedance, polarisation isolation and field patterns illustrate the design idea introduced and support the results of simulations.