Algorithm 1 in Guilbaud (2012, p. 327) in Biometrical Journal (DOI: 10.1002/bimj.201100123) reproduced a recently detected index error in a theorem concerning a shortcut for rejection decisions for certain multiple-testing procedures as it was stated in Bernhard et al. (2004, p. 8) in Statistical Papers (DOI: 10.1007/BF02778266). This short article provides: (i) the correction to be made to Algorithm 1 and (ii) a brief discussion of the consequences. Although the theoretical developments in Guilbaud (2012) are not affected, the numerical illustrations in Section 7 are affected. A corrected version of that section is given in the Supporting Information.