The purpose of this study is to assess the safety/tolerability and determine the Japanese recommended dose (RD) of bortezomib administered as a once-daily intravenous bolus twice weekly for 2 consecutive weeks(Days 1, 4, 8, and 11) followed by a 10-day rest period (Days 12 to 21) in Japanese patients with relapsed or refractory multiple myeloma.

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.

Based on the body surface area calculated before treatment in each cycle, the dose is calculated for each patient according to the dose level specified by the Patient Enrollment Center (0.7mg/m2, 1.0 mg/m2 or 1.3 mg/m2). JNJ-26866138 is intravenously administered once daily, twice weekly for 2 weeks (Days 1, 4, 8, and 11), followed by a 10-day rest period (Days 12 to 21). This is considered one cycle (21 days), and treatment is repeated up to 6 cycles in patients expected to show a response.

Inclusion Criteria:

• Patients diagnosed with multiple myeloma based on the predetermined diagnostic criteria
• Patients who received at least standard first-line therapy and had documentation of failure to that therapy or relapsed after remission and currently requires therapy because of progressive disease (PD) as assessed by the investigator (subinvestigator) at enrollment. There is no limitation in the number of prior therapies (salvage therapies
• Number of regimens)
• Patients with measurable disease, defined as follows: Secretory Multiple myeloma: Quantifiable serum monoclonal protein value (in general, serum M protein values of >= 1.0 g/dL of IgG and >= 0.5 g/dL of IgA.), When M protein is excreted in urine, M protein is quantitatively assayable by urinary protein electrophoresis (in general, urinary M protein excretion of >= 0.2g/day.). Non-secretory Multiple myeloma: Presence of bidimensionally measurable soft tissue masses (plasmacytomas) with a longer diameter of 2cm and more as determined by applicable radiographies (i.e. MRI, CT-scan)
• Patients with a life expectancy of >= 3 months after initiation of JNJ-26866138 therapy
• Patients with a Karnofsky Performance Status (PS, general condition) of >= 60
• Patients aged >=20 and =< 75 at enrollment in the study
• Patients who can be hospitalized at least from the initial treatment of the study drug to the completion of Cycle 1 (including the 10-day observation period after JNJ-26866138 injection - when the next cycle is delayed because the "conditions for the start of the nextcycle" were not satisfied, patients must be hospitalized until the patient satisfies the criteria (it is possible to transfer patients to treatment on an outpatient basis when the next cycle is delayed due to reasons such as schedule adjustment

Exclusion Criteria:

• Patients with plasma cell leukemia (Definition of plasma cell leukemia: A state in which the proportion of plasma cells in peripheral blood is 20%, with their absolute count being more than 2x10 ^ 9L.)
• Patients with Crow-Fukase syndrome (multiple neuritis, pigmentation, endocrine disorder, swollen organ, sclerotic bone lesion and, etc.)
• Patients with peripheral sensory neuropathy of Grade 2 or worse ("neuropathy - sensory" in NCI-CTC Japanese translation JCOG version 2) or those with neuropathic pain of Grade 2 or worse ("neurologic pain" in NCI-CTC Japanese translation JCOG version)
• Patients who underwent allogeneic hematopoietic stem cell transplantation
• Patients who underwent two or more consecutive courses of autologous peripheral blood stem cell transplantation (tandem transplantation, etc.)
• Patients suspected of having cardiac amyloidosis (patients who had a left ventricular ejection fraction (LVEF) of less than 55% by echocardiogram)
• Patients with an active infection (fever of .38ºC)
• Patients with clinical findings of pneumonia (interstitial pneumonia) or pulmonary fibrosis or those having bilateral abnormal interstitial shadows (for example, ground-glass opacities, linear opacities) on chest CT (high resolution CT), regardless of the presence or absence of associated symptoms (consultation with specialists in the respiratory system or other fields was to be held if necessary)
• Patients with a heart disease of Class III or IV on the New York Heart Association (NYHA) cardiac function classification, patients who had myocardial infarction within 6 months prior to screening, or patients with uncontrolled angina pectris, serious ventricular arrhythmia, acute ischemia, active conduction disorder, or others
• Patients with a renal disease (chronic glomerulonephritis, diabetic nephropathy, hypertensive nephropathy, gouty nephropathy, etc.) leading to the onset of impaired renal function
• Patients with uncontrolled hypertension
• Patients on pharmacotherapy (oral hypoglycemic drug or insulin preparation) for diabetes mellitus