We propose a new model for the splicing of long introns, which we call intrasplicing. The basic idea of this model is that the splicing of long introns may be facilitated by the splicing of inner parts of the intron prior to the splicing of the long intron itself. Since long introns have up to about 100,000 bases, this model seems to be a likely explanation of their splicing. To investigate the possibility of this model, we develop a new computational method for the analysis of DNA sequences with respect to splicing. We analyze the genomic sequence of four species with our method and derive several results indicating that intrasplicing may be an appropriate model for the splicing of at least part of the long intron sequences.