The Holm-Bonferroni procedure (Holm, 1979) is a step-down sequentially rejective multiple-testing method that controls the family-wise error rate (FWER) at level $\alpha$ for any joint distribution of the test statistics, and is uniformly at least as powerful as the single-step Bonferroni correction. Given $m$ raw $p$-values, sort them in ascending order $p_{(1)} \leq p_{(2)} \leq \dots \leq p_{(m)}$ with associated hypotheses $H_{(1)}, \dots, H_{(m)}$. Starting at $i = 1$, reject $H_{(i)}$ if $p_{(i)} \leq \frac{\alpha}{m - i + 1}$ and proceed to $i+1$; at the first index where the inequality fails, stop and retain all remaining hypotheses $H_{(i)}, \dots, H_{(m)}$. The cascade of thresholds $\alpha/m, \alpha/(m-1), \dots, \alpha/1$ replaces Bonferroni's flat $\alpha/m$ threshold while preserving strong FWER control, so within a pre-specified comparison family only the surviving rejections are claimed as significant.