Some group II introns are mobile elements as well as catalytic RNAs. Introns aI1 and aI2 found in the gene COX1 in yeast mitochondria encode reverse transcriptases which promote site-specific insertion of the intron into intronless alleles ('homing'). For aI2 this predominantly occurs by reverse transcription of unspliced precursor RNA at a break in double-strand DNA made by an endonuclease encoded by the intron. The aI2 endonuclease involves both the excised intron RNA, which cleaves the DNA's sense strand by partial reverse splicing; and the intron-encoded reverse transcriptase which cleaves the anti-sense strand. Here we show that aI1 encodes an analogous endonuclease specific for a different target site compatible with the different exon-binding sequences of the intron RNA. Over half of aI1 undergoes complete reverse splicing in vitro, thus integrating linear intron RNA directly into the DNA. This unprecedented reaction has implications for both intron mobility and evolution, and potential genetic engineering applications.