We show that human stefin B, a protease inhibitor from the family of cystatins, is a copper binding protein, unlike stefin A. We have used isothermal titration calorimetry to directly monitor the binding event at pH 7 and pH 5. At pH 7 stefin B shows a picomolar affinity for copper but at pH 5 the affinity is in the nanomolar range. There is no difference in the affinity of copper between the wildtype stefin B (E31 isoform) and a variant (Y31 isoform), whereas the mutant (P79S), which is tetrameric, does not bind copper. The conformation of stefin B remains unaltered by copper binding. It is known that below pH 5 stefin B undergoes a conformational change and amyloid fibril formation. We show that copper binding inhibits the amyloid fibril formation and, to a lesser degree, the initial aggregation. Similarities to and differences from other copper binding amyloidogenic proteins are discussed.