The purpose of this study is to evaluate response rate, survival, safety and tolerability of YM155 given in combination with rituximab in subjects with Non-Hodgkin's Lymphoma.

This is an outpatient study. All subjects enrolled in this study will receive YM155 and rituximab given during 14 day cycles. Each subject will be assessed at the end of each cycle to determine if he or she may continue to the next cycle. Each subject will be eligible to continue receiving the combination regimen in this study until one of the discontinuation criteria is met.

If a subject discontinues treatment without progressive disease (PD) that subject will complete follow-up visits every 12 weeks for 1 year or until initiating another systemic anti-lymphoma treatment, exhibiting PD, or death.

Each subject will be contacted by the study site every 12 weeks for survival following the End of Treatment Visit. The contacts will continue until death or for no more than 1 year.

Inclusion Criteria:

• Any stage, histologically confirmed CD20-positive primary or transformed diffuse large B cell lymphoma (DLBCL)or grade 3 follicular lymphoma (FL)
• Ineligible for or have previously received an autologous stem cell transplant (ASCT)
• Relapsed following receipt of the last dose of systemic chemotherapy or ASCT
• At least one prior chemotherapy regimen. Prior chemotherapy regimen must have contained anthracycline (unless contraindicated)
• If the subject is female, she must be non-pregnant and non-lactating at the Baseline Visit. All sexually active males and females of childbearing potential must agree to use an adequate method of contraception throughout the study period
• Eastern Cooperative Oncology Group (ECOG) performance status \