We published a new method (BMC Bioinformatics 2014, 15:14) for searching for differentially expressed genes from two biological conditions datasets. The presentation of theorem 1 in this paper was incomplete. We received an anonymous comment about our publication that motivates the present work. Here, we present a complementary result which is necessary from the theoretical point of view to demonstrate our theorem. We also show that this result has no negative impact on our conclusions obtained with synthetic and experimental microarrays datasets.