Background: Many randomized trials involve missing binary outcomes. Although many previous adjustments for missing binary outcomes have been proposed, none of these makes explicit use of randomization to bound the bias when the data are not missing at random. Methods: We propose a novel approach that uses the randomization distribution to compute the anticipated maximum bias when missing at random does not hold due to an unobserved binary covariate (implying that missingness depends on outcome and treatment group). The anticipated maximum bias equals the product of two factors: (a) the anticipated maximum bias re were complete confounding of the unobserved covariate with treatment group among subjects with an observed outcome and (b) an upper bound factor that depends only on the fraction missing in each randomization group. If less than 15% of subjects are missing in each group, the upper bound factor is less than .18. Results: We illustrated the methodology using data from the Polyp Prevention Trial. We anticipated a maximum bias under complete confounding of .25. With only 7% and 9% missing in each arm, the upper bound factor, after adjusting for age and sex, was .10. The anticipated maximum bias of .25 × .10 =.025 would not have affected the conclusion of no treatment effect. Conclusion: This approach is easy to implement and is particularly informative when less than 15% of subjects are missing in each arm.