I describe the self-splicing of an RNA that consists of exon sequences flanked by group II intron sequences. I find that this RNA undergoes accurate splicing in vitro, yielding an excised exon circle. This splicing reaction involves the joining of the 5' splice site at the end of an exon to the 3' splice site at the beginning of the same exon; thus, I term it inverse splicing. Inverse splicing provides a potential mechanism for exon scrambling, for exon deletion in alternative splicing pathways, and for exon shuffling in gene evolution.