This paper introduces an algorithm for finding eukaryotic genes. It particularly addresses the problem of orphan genes, that is of genes that cannot, based on homology alone, be connected to any known gene family and to which it is therefore not possible to apply traditional gene finding methods. To the best of our knowledge, this is also the first algorithm that attempts to compare in an exact way two DNA sequences that contain both coding (i.e. exonic) and non-coding (i.e. intronic and, possibly, intergenic) parts. The comparison is performed following an algorithmical model of a gene that is as close as possible to the biological one (we consider in this paper the “one ORF, one gene” problem only). A gene is seen as a set of exons that are pieces of an assembly and are not independent. The algorithm is efficient enough: although the constants are higher than for usual sequence comparison, its time complexity is proportional to the product of the sequences lengths while its space complexity scales linearly with the length of the smallest sequence.