A novel method to design a compact, broadband circularly polarised square slot antenna (CPSSA) with a considerably wide axial ratio (AR) bandwidth is proposed. A coplanar waveguide fed square slot antenna with an impedance matching stub and a cross-shape radiating patch together with a strip line that connects the two opposite corners of the ground section is designed to provide the desired characteristics. The obtained results for the proposed antenna provide good agreement with the expected performance with a compact size of 20 x 20 mm. The measured impedance bandwidth is as large as 11 050 MHz (2950-14 000 MHz) or about 130.38% with respect to the centre frequency. The measured 3 dB AR is 3373 MHz (35.7%) from 3729 to 7102 MHz and the average measured gain of the CPSSA is almost 3.5 dBi in the operating band.