We consider construction of a characteristic distribution of an L-tuple in a DNA sequence. The mathematical characteristic of the characteristic distribution is selected as invariant to characterize the L-tuple. With the invariant, we can perform the sequence comparison. The graphs of characteristic distributions of dinucleotide GC for the coding sequences of the first exon of β-globin gene of eleven different species and the construction of phylogenetic tree of twenty four coronavirus genomes illustrate the utility of the approach.