Regulatory factor X (RFX) proteins are transcriptional activators that recognize X-boxes (DNA of the sequence 5′-GTNRCC(0–3N)RGYAAC-3′, where N is any nucleotide, R is a purine and Y is a pyrimidine) using a highly conserved 76-residue DNA-binding domain (DBD). DNA-binding defects in the protein RFX5 cause bare lymphocyte syndrome or major histocompatibility antigen class II deficiency. RFX1, -2 and -3 regulate expression of other medically important gene products (for example, interleukin-5 receptor α chain, IL-5Rα). Fusions of the ligand-binding domain of the oestrogen receptor with the DBD of RFX4 occur in some human breast tumours. Here we present a 1.5 Å-resolution structure of two copies of the DBD of human RFX1 (hRFX1) binding cooperatively to a symmetrical X-box^,. hRFX1 is an unusual member of the winged-helix subfamily of helix–turn–helix proteins because it uses a β-hairpin (or wing) to recognize DNA instead of the recognition helix typical of helix–turn–helix proteins. A new model for interactions between linker histones and DNA is proposed.