The expected duration of this study is 2.5 years. All participants will receive two intravenous infusions of rituximab in an outpatient setting at study entry and Week 2. Throughout the study, participants will receive MTX, systemic corticosteroids, and folic or folinic acid. MTX dosing will be re-evaluated by disease activity scores every month until Month 6 and again at Months 8, 10, and 12. Systemic corticosteroid doses will be modified based on the participant's health while in the study. Use of nonsteroidal anti-inflammatory drugs (NSAIDs) is permitted, but NSAID doses should not be changed during the study, if at all possible. NSAIDs will not be provided by this study.