Numerous high-throughput sequencing studies have focused on detecting conventionally spliced mRNAs in RNA-seq data. However, non-standard RNAs arising through gene fusion, circularization or trans-splicing are often neglected. We introduce a novel, unbiased algorithm to detect splice junctions from single-end cDNA sequences. In contrast to other methods, our approach accommodates multi-junction structures. Our method compares favorably with competing tools for conventionally spliced mRNAs and, with a gain of up to 40% of recall, systematically outperforms them on reads with multiple splits, trans-splicing and circular products.