Sequencing by hybridization allows the reconstruction of the DNA string of a given length from smaller fragments. These fragments are obtained in the hybridization experiment in which the DNA hybridizes to a DNA chip. In a classical approach, the chip consists of all oligonucleotides of a given length, with only one type of oligonucleotide for each probe of the chip. In this paper, we propose an algorithm solving the non-classical case of SBH, where the chip probes consist set of oligonucleotides described by some specific pattern. We will present the definition of such a non-classical DNA chip and the algorithm solving a sequencing problem related to such a chip. Unlike recent metaheuristic approaches to the classical SBH problem, the proposed algorithm tries to find an exact sequence, and even in the presence of all the hybridization errors in spectrum is very often able to do so in a short time. If only negative errors from repetitions are allowed, then the algorithm is able to reconstruct sequences having length of thousands nucleotides.