The study is directed to patients with PBC diagnosis who have had management with standard UDCA dose (13 to 15 mg/kg per day) for at least 6 months and had not reached complete biochemical response, defined by Paris II criteria. The dose of fibrate to use will be bezafibrate 200 mg every 12 hours or placebo every 12 hours for 12 months, both having the exact characteristics to avoid their recognition. Patients will continue the administration of UDCA at the same dose at enrollment. The intervention will be for a period of 12 months, with a follow-up every 3 months completing 5 medical follow-up visits (0, 3, 6, 9 and 12 months).