A new fractal technique is applied to hair-pin microstrip bandpass filters for the second spurious suppression. The coupled edges of hair-pin microstrip resonators are changed by a new fractal to equalise the odd-mode and even-mode phase velocities so that the nearest spurious harmonic can be suppressed. Simulated and measured results show that the second spurious level is reduced below 30dB for a 1GHz and 25 bandwidth bandpass filter. An analysis is presented to show the effects of tap point height on fundamental parameters of the filters. In addition, the circuit size is reduced by 11 in comparison to the conventional filter.