Higher harmonics in current-phase relations of Josephson Junctions are predicted to be observed when the first harmonic is suppressed. Conventional theoretical models predict higher harmonics to be extremely sensitive to changes in barrier thickness, temperature, and so on. Here we report experiments with Josephson junctions incorporating a spin-dependent tunnelling barrier, revealing a current-phase relation for highly spin polarized barriers that is purely second harmonic in nature and is insensitive to changes in barrier thickness. This observation implies that the standard theory of Cooper pair transport through tunnelling barriers is not applicable for spin-dependent tunnelling barriers.