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In this paper, we propose considering an exact likelihood score (ELS) test for non-inferiority comparison and we derive its test-based confidence interval for the difference between two independent binomial proportions. The p-value for this test is obtained by using exact binomial probabilities with the nuisance parameter being replaced by its restricted maximum likelihood estimate. Calculated type I errors revealed that the proposed ELS method has important advantages for non-inferiority comparisons over popular asymptotic methods for adequately powered confirmatory clinical trials, at 80% or 90% statistical power. For unbalanced sample sizes of the compared treatment groups, the type I errors for the asymptotic score method were shown to be higher than the nominal level in a systematic pattern over a range of the true proportions, but the ELS method did not suffer from such a problem. On average, the true type I error of the ELS method was closer to the nominal level than all considered methods in the empirical comparisons. Also, in rare cases, the type I errors of the ELS test exceeded the nominal level, but only by a small amount. In addition, the p-value and confidence interval using the ELS method can be obtained in less than 30 seconds of computer time for most confirmatory trials. The theoretical arguments and the attractive empirical evidence, along with fast computation time, should make the ELS method very attractive for consideration in statistical practice.