Chemical "addressed" modification of DNA involves treatment of single-stranded DNA with oligonucleotides complementary to certain target sequences in this DNA and bearing a groupings reactive towards DNA bases. The binding of oligonucleotides can occur both at completely (specific) and incompletely (nonspecific) complementary sites. We analyse the modification of a fragment that is flanked by two target sequences complementary to a given oligonucleotide address, contains no more such targets and has some randomly distributed sites for nonspecific binding. Conditions for the maximum ratio between specific and non-specific modification are determined. We find the probability of both target termini being specifically modified without any non-specific modification occurring within the fragment up to a given moment in time. Quantitative analysis is based on the use of known features of the specific and non-specific binding of an oligonucleotide to DNA sites. This analysis shows the possibility of specific cutting of DNA based on addressed modification.