The arrangement of the alternately symmetrical unit cells of an H-shaped slot fractal uniplanar electromagnetic bandgap structure (HSF-UC-EBGs) is investigated in this study. It is shown that different bandgap characteristics can be obtained when the unit cells are arranged in different ways. Two bandgaps of 1.30–2.52 and 2.85–3.76 GHz are obtained when 5 unit cells are arranged along x direction, while a bandgap of 2.30–4.78 GHz is obtained when 5 unit cells are arranged along y direction. Therefore, one can predict that when the symmetrical unit cells and the 90° rotated symmetrical unit cells are arranged alternately, the bandgap will extend to the sum of the three bandgaps mentioned previously. Based on the study described previously, we design an ultra-wideband quasi-isotropic HSF-UC-EBGs and the measured results show that its relative bandwidth reach up to at least 105.4% GHz at 3.32 GHz.