We introduce a robust likelihood approach to inference for paired multiple binary endpoints data. One can easily implement the innovative methodology without dealing with the model that incorporates a large number of joint probabilities of no direct relevance to the inference of interest. We present the robust score test statistic for testing the equality of two treatment effects to exemplify the utility and simplicity of the method. Our novel technique is reproducible in that patients could have different numbers of endpoints and need not be paired. We use simulations and real data analysis to highlight the efficacy of our robust procedure.