By using a photoemission electron microscope in combination with X-ray magnetic circular dichroism, the domain configuration in a single crystalline Co film exchange coupled to an Fe₅₀Mn₅₀ film is obtained. The effect of the ferromagnetic/antiferromagnetic interaction is observed to be different in Co domains with different magnetization direction, establishing the fact that the exchange bias is locally set by the magnetization of the ferromagnetic layer, without external field.