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Background: Bimekizumab is a monoclonal IgG1 antibody that selectively inhibits interleukin (IL)-17F and IL-17A. This study compared the efficacy and safety of bimekizumab with placebo over 16 weeks in patients with active psoriatic arthritis and previous inadequate response or intolerance to tumour necrosis factor-α (TNFα) inhibitors. Methods: BE COMPLETE was a phase 3, multicentre, randomised, double-blind, placebo-controlled trial conducted across 92 sites (including hospitals, clinics, and research centres) in 11 countries (Australia, Canada, Czech Republic, Germany, Hungary, Italy, Japan, Poland, Russia, the UK, and the USA). Eligible patients were aged 18 years or older with adult-onset psoriatic arthritis (meeting the Classification Criteria for Psoriatic Arthritis for at least 6 months before screening) with a history of inadequate response or intolerance to treatment with one or two TNFα inhibitors for either psoriatic arthritis or psoriasis. We stratified patients with active psoriatic arthritis by region and previous TNFα inhibitor use. Patients were randomly assigned (2:1) to receive subcutaneous bimekizumab 160 mg every 4 weeks or placebo by an interactive-voice and web-response system on the basis of a predetermined randomisation schedule. The primary endpoint was the proportion of patients with 50% or greater improvement in American College of Rheumatology criteria (ACR50) at week 16 (non-responder imputation). Efficacy analyses were done in the randomised population. The safety analysis set comprised patients who received one or more doses of study treatment. This trial was registered at ClinicalTrials.gov, NCT03896581, and is completed. Findings: Between March 28, 2019, and Feb 14, 2022, 556 patients were screened and 400 patients were randomly assigned to bimekizumab 160 mg every 4 weeks (n=267) or placebo (n=133). The primary and all hierarchical secondary endpoints were met at week 16. 116 (43%) of 267 patients receiving bimekizumab reached ACR50, compared with nine (7%) of 133 patients receiving placebo (adjusted odds ratio [OR] 11·1 [95% CI 5·4–23·0], p Interpretation: Bimekizumab treatment led to superior improvements in joint and skin efficacy outcomes at week 16 compared with placebo in patients with psoriatic arthritis and inadequate response or intolerance to TNFα inhibitors. The safety profile of bimekizumab was consistent with previous phase 3 studies in patients with plaque psoriasis, and studies of IL-17A inhibitors.