Trans-splicing is an unusual process in which two separate RNA strands are spliced together to yield a mature mRNA. We present a novel computational approach which has an overall accuracy of 82% and can predict 92% of known trans-splicing sites. We have applied our method to Chromosomes 1 and 3 of Leishmania major, with high confidence predictions for 85% and 88% of annotated genes respectively. We suggest some extensions of our method to other systems.