This is a randomized, placebo-controlled, parallel-group study designed to enroll a total of 34 patients with diagnosis of PBC without a complete response to the use of UDCA for more than a year, then the participants will be divided by randomization to receive bezafibrate or placebo, resulting in a total of two groups of 17 patients each. Both groups will be followed every 3 months for a total of 1 year with clinical and laboratory follow-up to determine the efficacy and security of the treatment. The investigators will measure all the laboratory variables related to the disease and possible adverse effects of the use of fibrates (creatine kinase, transaminases, bilirubin, alkaline phosphatase), also the investigators will measure the quality of life variables (pruritus severity, Short Form [SF]-36 questionnaire), and determine the fibrosis stage at the beginning and end of the study by non-invasive methods (transient elastography).