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We have studied the effects on the exchange bias of decreasing the antiferromagnetic layer to the Angström-scale regime in order to shed light on the minimum required thickness of the antiferromagnet. We have deposited IrMn layers between 0.2 and 2 nm on spin valves and measured the exchange bias by examining hysteresis loops at 5 K using the giant magnetoresistance of the spin valves. The exchange bias persists for IrMn thicknesses down to 0.4 nm and has a maximum at 1.6 nm. Because the ultra-thin layers create an exchange field, the origin of at least one component of exchange biasing must have a similarly short length scale.