<p>In clinical trials, multiple correlated continuous and binary variables are often employed as primary endpoints, and evaluation using multiple endpoints establishes evidence for the efficacy of the test treatment. When dealing with multiple endpoints, the familywise error rate of statistical tests must be kept below the nominal significance level. In several studies, procedures have been developed that can be applied to multiple primary endpoints with only a superiority test. However, a procedure that simultaneously incorporates non-inferiority and superiority tests and includes multiple continuous as well as binary variables has not yet been discussed. In this study, we propose a testing procedure that recognizes the efficacy of test treatment only when the superiority of at least one endpoint and the non-inferiority of the remaining endpoints are achieved. The type I error rates and powers of the proposed testing procedure are evaluated through simulations and are compared with those of the closed testing procedure. Regardless of the correlation between endpoints, sample size, or the magnitude of the difference between endpoints in the two groups, the type I error rate was shown not to be inflated. The proposed testing procedure showed higher power than the closed testing procedure. When any of the endpoints are within the non-inferiority margin, the power is drastically reduced depending on the correlation coefficient, indicating the importance of obtaining reliable information a priori.</p>