The physics behind the evolution of exchange bias in systems with uniaxial magnetic anisotropy is of high scientific and technological importance. We show unexpected behaviour of exchange bias with decreasing temperature for epitaxially grown hcp in plane c-axis Co/CoO structure, with uniaxial magnetic anisotropy. We observe a temperature-dependent increase of exchange bias in three distinct steps. This is most pronounced in the hard axis magnetisation direction, overall showing striking differences when compared with polycrystalline isotropic multilayer. The steps correspond to three peaks in coercivity as oppose to one peak around the blocking temperature usually expected and observed in other experiments. We would like to investigate the link between anomalous trend of exchange bias and magnetic profile of a multilayer using polarised neutron reflectivity measurements.