AbstractNormalization of single cell RNA-seq data remains a challenging task. The performance of different methods can vary greatly between datasets when unwanted factors and biology are associated. Most normalization methods also only remove the effects of unwanted variation for the cell embedding but not from gene-level data typically used for differential expression (DE) analysis to identify marker genes. We propose RUV-III-NB, a method that can be used to remove unwanted variation from both the cell embedding and gene-level counts. Using pseudo-replicates, RUV-III-NB explicitly takes into account potential association with biology when removing unwanted variation. The method can be used for both UMI or read counts and returns adjusted counts that can be used for downstream analyses such as clustering, DE and pseudotime analyses. Using published datasets with different technological platforms, kinds of biology and levels of association between biology and unwanted variation, we show that RUV-III-NB manages to remove library size and batch effects, strengthen biological signals, improve DE analyses, and lead to results exhibiting greater concordance with independent datasets of the same kind. The performance of RUV-III-NB is consistent and is not sensitive to the number of factors assumed to contribute to the unwanted variation.