Inclusion Criteria:  Adult subjects (≥ 18 years old) < 75 years old Dermatomyositis defined according to the 239th ENMC criteria  Active disease (ACR/EULAR criteria) defined as :  Manual Muscle Testing (MMT-8) <145/150 and at least two additional abnormal corset measurements (CSM): >3/10 cm on Visual Analogue Scale (VAS) of patient global, physician global and extra-muscular disease activity, Health Assessment Questionnaire Disability Index >0.25, or elevated muscle enzymes. Or cutaneous CDASI > 20 and at least two additional abnormal corset measurements (CSM): >3/10 cm on Visual Analogue Scale (VAS) of patient global, physician global and extra-muscular disease activity, Health Assessment Questionnaire Disability Index >0.25, or elevated muscle enzymes  for relapsing DM patients :  in case of corticosteroid exposure patient must receive a stable dose < 30 mg/d prednisone with or without additional immunosuppressive therapy for at least 4 weeks before the baseline visit. Stable dose of immunosuppressive therapy for at least 3 months before Affiliation to a social security regime Written informed consent  Exclusion Criteria:  Life-threatening complications :  Severe swallowing troubles defined as: food swallowed the wrong way and/or time to drink a glass of 200 ml water above 30 seconds Interstitial lung disease related to the DM with one among the following complications (complications must be related to the ILD): dyspnea NYHA III, hypoxemia with PaO2≤65 mmHg, and/or DLCOc/Alveolar Volume ≤70% (pulmonary function test) Symptomatic myocarditis o Loss of walking ability Deep vein thrombosis/pulmonary embolism in past medical history in absence of anticoagulant Pregnant or lactating, or women planning to become pregnant or initiating breastfeeding No effective contraception during the study and one week after for women of childbearing age Renal impairment defined as clearance < 60 ml Strong Organic Anion Transporter 3 (OAT3) inhibitors A new cancer or malignancy except for basal and squamous cell carcinoma of the skin or in situ carcinoma of the cervix treated and considered cured by the investigator Active severe infection including active hepatitis Evidence of latent tuberculosis (as documented by a positive QuantiFERON-TB Gold plus test) Absolute Neutrophil Count < 1x109 cells/L Haemoglobin (Hb) < 8 g/dL Liver insufficiency (Prothrombin time <60%)  Previous treatment exposure relating to the treatment/procedures : • Rituximab treatment within 6months before inclusion  IVIg, or cyclophosphamide infusion within the month before inclusion both methotrexate (0.3 mg/kg/w) and azathioprine exposure for at least 3 months each and at the 0.3 mg/kg/w and 2-3 mg/kg/d dosages respectively. (but exposure to either of these two drugs alone is not an exclusionary criterion) more than 2 weeks treatment duration with corticosteroids at the dose of 1 mg/kg/d before the inclusion. Hypersensitivity to the active substance (baricitinib) or to any of the excipients Conditions affecting the outcomes (Expected poor compliance) Severe disease damages: e.g. muscle weakness mainly related to muscle damage such as fat replacement of muscle) defined as persistent changes in anatomy, physiology, pathology or function which result from previously active disease and from complications of therapy or other events (e.g.; muscle atrophy, fatty replacement; skin skars, poilkilodermy). Severe disease damage is considered when the patient condition has no or minor ability to improve with the treatment. Significant uncontrolled cardiovascular, cerebrovascular, respiratory, hepatic, renal, gastrointestinal, endocrine, hematologic, or neuropsychiatric disorders, or abnormal laboratory values that developed during a qualifying study that, in the opinion of the investigator, poses an unacceptable risk for the patient's participation Chest imaging (CT scan or radiograph) showing abnormalities not related with the DM in the last 12 weeks judged by the investigator as clinically significant. Diagnosis of Covid 19 infection (SARSCoV-2 positive PCR) Participants included in other intervention research involving humans Patient under tutorship or guardianship, and incapable to give informed consent