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This paper presents a novel method for size reduction of patch antennas by introducing an irregular ground structure to provide capacitive and inductive loading to the patch. Each of the four corners of the square patch is assigned with a pair of metallic walls. These special metallic walls located underneath the patch are constructed and integrated within the microwave substrate by connected vias. The vertical portion of the walls introduces the inductance whereas the separation between the two parallel walls creates the capacitance. Additional capacitances are also created between the flat strips connecting the vias and the radiating patch. No modifications are made to the square patch. With the presence of the substrate integrated irregular ground (SIIG) structure, the antenna finds a significant size reduction by the capacitive and inductive loading effect. For the proposed linearly-polarized antenna operating at 2.635 GHz, we achieve a total patch area reduction of 75.6% experimentally when compared with a half-wavelength patch antenna loaded with the same substrate. Furthermore, by using two sets of connecting strips with different lengths, two orthogonal modes are excited for circular polarization and similar size reduction effect is achieved.