A new technique for tripling the frequency of a microwave signal is presented. It is based on an integrated dual-parallel Mach Zehnder modulator, which generates two orthogonally polarised RF modulated optical signals with different modulation indexes, and a polarisation dependent optical attenuator. The photodetector output fundamental RF components generated by the two orthogonally polarised RF modulated optical signals have the same amplitude but an opposite phase, which are cancelled, leaving the frequency tripled microwave signal and the unwanted fifth order harmonic. The new frequency tripler has a simple structure, a wide bandwidth and a high electrical spurious suppression ratio. Experimental results are presented demonstrating three times frequency multiplication of different-frequency microwave signals with electrical spurious suppression ratio of over 20 dB. The phase noise and the stability performance of the frequency tripler are also investigated experimentally.