A design procedure for a circularly polarised 2 × 2 patch antenna array is presented. The structure involves 22 design parameters with associated constraints, and a multi-objective genetic algorithm is developed to determine the parameter values. This approach removes the requirement for quarter-wave transformers associated with the conventional method, and achieves a more compact configuration. In addition, the proposed design reduces step discontinuities and hence reduces spurious radiation. The related constraints were the lengths, characteristic impedance values of the array feed network and the phase-shifting between the radiating elements of the array. The return loss and axial ratio for a 5.8 GHz array were investigated and good agreement was obtained between calculated, simulated, and measured measurements.