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 \</= 1

Exclusion Criteria:

* Use of any standard/experimental anti-lymphoma drug therapy within 21 days of the Baseline Visit
* Use of systemic steroids within 5 days of the Baseline Visit (except for the purposes of pre-medication prior to study regimen treatment)
* Prior allogeneic stem cell transplant (SCT)
* The subject has been previously treated with YM155
* The subject has known human immunodeficiency virus (HIV), hepatitis B surface antigen, or hepatitis C antibody
* The subject has received other investigational therapy or procedures within 21 days prior to the first study drug administration