Summary Exact unconditional tests have been widely applied to test the difference between two probabilities for 2 × 2 matched‐pairs binary data with small sample size. In this context, Lloyd (2008, Biometrics64, 716–723) proposed an E + Mp‐value, that showed better performance than the existing Mp‐value
and Cp‐value. However, the analytical calculation of the E + Mp‐value requires that the Barnard convexity condition be satisfied;
this can be challenging to prove theoretically. In this article, by a simple reformulation, we show that a weaker condition, conditional monotonicity, is sufficient to calculate all three p‐values (M, C,
and E + M) and their corresponding exact sizes. Moreover, this conditional monotonicity condition is applicable to noninferiority tests.