This open-label study will assess anti-tumor activity and safety of belinostat in combination with bortezomib (Velcade®) in multiple myeloma patients refractory to or relapsed from at least one prior bortezomib-containing regimen. Subjects will be administered both PXD101 and bortezomib on the same days: i.e. days 1, 4, 8, and 11 of a 3-week cycle, for up to 8 cycles.