In the Holm-Bonferroni method (Holm, 1979), the P-values are first sorted and then the smallest value is multiplied by N, where N is the total number of genes being tested. The next value is then multiplied by N-1 and so on, so that the last P-value is multiplied by 1.
This method is not as conservative as the Bonferroni method, but may still exclude many potentially interesting genes (false negatives). As with the Bonferroni method, the Holm-Bonferroni method may be best utilized when looking for a small number of genes for further experiments which are highly differentially expressed. In other words, this method can be effective when the goal is to just eliminate false positives even if it is at the cost of a number of false negatives.