Facioscapulohumeral dystrophy (FSHD, OMIM: 158900, 158901) is the most common dystrophy in adults and so far, there is no treatment. Different loci of the disease have been characterized and they all lead to the aberrant expression of the DUX4 protein, which impairs the function of the muscle, ultimately leading to cell death. Here, we used gene editing to try to permanently shut down DUX4 expression by targeting its poly(A) sequence. We used transcription activator-like effector nucleases (TALEN) and CRISPR-Cas9 nucleases in vitro on FSHD myoblasts. More than 150 TOPO clones were sequenced and only indels were observed in 4%. Importantly, in 2 of them, the DUX4 poly(A) signal was eliminated at the genomic level but DUX4 mRNA was still produced thanks to the use of a non-canonical upstream poly(A) signal sequence. These experiments show that targeting DUX4 PAS at the genomic level might not be an appropriate gene editing strategy for FSHD therapy.