Ubiquitin-binding protein that specifically recognizes and binds 'Lys-63'-linked ubiquitin. Plays a central role in the BRCA1-A complex by specifically binding 'Lys-63'-linked ubiquitinated histones H2A and H2AX at DNA lesions sites, leading to target the brca1-bard1 heterodimer to sites of DNA damage at double-strand breaks (DSBs). The BRCA1-A complex also possesses deubiquitinase activity that specifically removes 'Lys-63'-linked ubiquitin on histones H2A and H2AX. Also weakly binds monoubiquitin but with much less affinity than 'Lys-63'-linked ubiquitin (By similarity). Component of the BRCA1-A complex. Localizes at sites of DNA damage at double-strand breaks (DSBs). The tandem UIM domains form a continuous 60 Angstrom-long alpha-helix and mediate binding to 'Lys-63'-linked ubiquitins. UIM1 and UIM2 bind to the proximal and distal ubiquitin moieties and recognize an 'Ile-44'-centered hydrophobic patch. Since UIMs don't interact with the 'Lys-63' isopeptide bond the UIM-linker region between the 2 UIM domains determines the selectivity for 'Lys-63'-linkage, and its length is very important for specificity (By similarity). Belongs to the RAP80 family.