Generating correlated binary data with specified marginal probabilities and correlation structure is often needed and useful in simulation studies to investigate the finite sample performance of statistical methods. Conditional linear family provides a powerful and flexible tool to generate correlated matched-pair binary data including the physician–patients and clustered match-pair data. To ensure the validity of the data generation process, constraints for parameters of the conditional linear family are needed. For the correlated matched-pair binary data with an exchangeable-type correlation structure, we derive the explicit expressions to check these constraints and it provides an efficient and convenient computational tool in validating the data generation process. The results are applied to check the constraints for two typical correlated matched-pair binary data.