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The effect of patterning on the shift of the hysteresis loop HE and coercivityHC in a system composed of two perpendicularly exchange-coupled ferromagnets (NiFe sputtered onto a [Pt/Co] multilayer) is investigated in long stripes and square dots. Setting the exchange bias coupling along the stripes results in a threefold increase of HE compared to the continuous films. HC increases dramatically when the coupling is set perpendicular to the stripes and also in the dots. Magnetic force microscopy studies and micromagnetic simulations suggest that differences in the number and orientation of the magnetic domains can account for the observed effects.