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The magnetization process in a square dot of permalloy having a size of 20 μm and 80 nm thickness has been investigated with a focused magneto-optical hysteresigraph. With this apparatus, it is possible to measure in a few seconds the hysteresis loop with a signal-to-noise ratio adequate for the observation of Barkhausen jumps also in such a small magnetic sample. From a sequence of 6000 loops, systematic data on the statistical properties of these jumps have been extracted. The observed behavior shows strong deviations with respect to the available data on bulk samples and thin films.