The ubiquitin-specific processing protease (UBP) family of deubiquitinating enzymes plays an essential role in numerous cellular processes. HAUSP, a representative UBP, specifically deubiquitinates and hence stabilizes the tumor suppressor protein p53. Here, we report the crystal structures of the 40 kDa catalytic core domain of HAUSP in isolation and in complex with ubiquitin aldehyde. These studies reveal that the UBP deubiquitinating enzymes exhibit a conserved three-domain architecture, comprising Fingers, Palm, and Thumb. The leaving ubiquitin moiety is specifically coordinated by the Fingers, with its C terminus placed in the active site between the Palm and the Thumb. Binding by ubiquitin aldehyde induces a drastic conformational change in the active site that realigns the catalytic triad residues for catalysis.