Patients eligible and willing to enter the study will be evaluated at baseline by isolation and study of frequency and absolute numbers of B cells and their function, biochemical and AMA tests. Histology and quality of life will be also evaluated in all patients. The methodology to be used for B cell study is already well-established in our laboratory as can be seen in the attached paper (Kikuchi et al. 2005b). Patients will be administered 1,000 mg rituximab intravenously by slow infusion on Day 1 and Day 15 (+/- 1 day). Rituximab's pharmacokinetics indicate that complete B cell depletion is obtained 2-3 days after administration and that such effect may be lost after 9 months (Vieira et al. 2004). In addition to our B cell work, serum samples will undergo AMA testing, including titers, using recombinant mitochondrial antigens (Miyakawa et al. 2001). Patients will also undergo serum chemistry panel, which includes liver function tests. Patients will continue on a steady dose of UDCA therapy throughout the study.