The SHOM method (Sequencing by Hybridization with Oligonucleotide Matrix) developed in 1988 is a new approach to nucleic acid sequencing by hybridization to a octanucleotide matrix composed of an array of immobilized oligonucleotides. The original matrix proposed for sequencing by SHOM had to contain at least 65,536 octanucleotides. The present work describes a new family of matrices for sequencing, which allows one to reduce the number of synthesized oligonucleotides 5-15 times without essentially decreasing the resolving power of the method.