In turbomachinery the joint between a turbine blade and the endwall often involves a fillet. Previous studies show that this fillet significantly influences the secondary flows despite regularly being omitted from simulation and testing, specifically that a uniform fillet radius of 16% axial chord increased endwall losses by 10%. It was proposed that a variable radius fillet could reduce secondary flows and the associated endwall losses. This paper describes a computational study to determine what variable radius fillet is required for optimal performance in the cascade. The variable radius fillet ranges from 0.5% to 16% of axial chord and was found using a genetic algorithm optimisation. Although this is a computational study the design offers physically plausible mechanisms by which the extra losses introduced by fillets may be reduced. This paper also suggests a generalised rule of fillet radius variation to minimise endwall losses. A large radius is required on the leading edge that reduces slowly along the pressure side but rapidly on the suction side such that the smallest permitted radius is applied to the suction side. A medium radius is required at the trailing edge
