It is realized that the first intron plays a key role in regulating gene expression, and the interactions between the first introns and other introns must be related to the regulation of gene expression. In this paper, the sequences of mitochondrial ribosomal protein genes were selected as the samples, based on the Smith-Waterman method, the optimal matched segments between the first intron and the reverse complementary sequences of other introns of each gene were obtained, and the characteristics of the optimal matched segments were analyzed. The results showed that the lengths and the ranges of length distributions of the optimal matched segments are increased along with the evolution of eukaryotes. For the distributions of the optimal matched segments with different GC contents, the peak values are decreased along with the evolution of eukaryotes, but the corresponding GC content of the peak values are increased along with the evolution of eukaryotes, it means most introns of higher organisms interact with each other though weak bonds binding. By comparing the lengths and matching rates of optimal matched segments with those of siRNA and miRNA, it is found that some optimal matched segments may be related to non-coding RNA with special biological functions, just like siRNA and miRNA, they may play an important role in the process of gene expression and regulation. For the relative position of the optimal matched segments, the peaks of relative position distributions of optimal matched segments are increased during the evolution of eukaryotes, and the positions of the first two peaks exhibit significant conservatism.