Many DNA-binding factors, such as transcription factors, form oligomeric complexes with structural symmetry that bind to palindromic DNA sequences1. Palindromic consensus nucleotide sequences are also found at the genomic integration sites of retroviruses2,​3,​4,​5,​6 and other transposable elements7,​8,​9, and it has been suggested that this palindromic consensus arises as a consequence of the structural symmetry in the integrase complex2,3. However, we show here that the palindromic consensus sequence is not present in individual integration sites of human T-cell lymphotropic virus type 1 (HTLV-1) and human immunodeficiency virus type 1 (HIV-1), but arises in the population average as a consequence of the existence of a non-palindromic nucleotide motif that occurs in approximately equal proportions on the plus strand and the minus strand of the host genome. We develop a generally applicable algorithm to sort the individual integration site sequences into plus-strand and minus-strand subpopulations, and use this to identify the integration site nucleotide motifs of five retroviruses of different genera: HTLV-1, HIV-1, murine leukaemia virus (MLV), avian sarcoma leucosis virus (ASLV) and prototype foamy virus (PFV). The results reveal a non-palindromic motif that is shared between these retroviruses.