In Japan, there is no clear treatment guidance for patients with multiple myeloma that repeatedly relapsed and became refractory. At present, various therapies including other multi-drug combination chemotherapy, hematopoietic stem cell transplantation, corticosteroid massive therapy, interferon therapy, thalidomide therapy, radiation therapy and other experimental therapies are conducted exploratory as salvage therapies to find the one to which the patient shows response. Considering that the antitumor activity of JNJ-26866138 against relapsed or refractory MM is clear and and the tolerability is acceptable based on results of the overseas clinical studies, the development of JNJ-26866138 in Japan is quite meaningful. This is a non-randomized, open-label, multicenter dose-escalation study which consisting of the two parts: the Phase I part is intended to intravenously administer JNJ-26866138 twice daily for 2 weeks (Days 1, 4, 8, and 11) to establish the Japanese RD based on the incidence of dose limiting toxicities (DLTs), while the Phase II part is intended to evaluate the efficacy and safety of JNJ-26866138 in patients repeatedly treated at the Japanese RD.