We examined the probability of short palindromec DNA sequences to occur as four-stranded structures held together in double-helical DNA by the additional hydrogen bonds postulated by McGavin (1971). The likeliness of the palindromes to be folded at their symmetry axes to allow the additional hydrogen bonding was considered using published physicochemical evidence and theoretical deductions. We deduced that both in vivo and in vitro the requirements may be met for duplex DNA folding which would approach palindrome complementary base bairs and thus allow the formation of the additional hydrogen bonds. However, we propose hydrogen bonding between guanine-cytosine base pairs to be different than that proposed by McGavin. Using CPK atom models we found that formation of the tertiary conformation already proposed by other authors and which we call the cage structure may be prevented or hindered by adenine, guanine or cytosine methylation. The available experimental data on recognition and cleavage site specificity of the Type 11 restriction endonucleases were confronted with the cage model as an alternative of the cruciform model and with the postulated effects of base methylation. The published data did not contradict the validity of the cage model and the role of base methylation in preventing the four-stranded palindrome structure. An applicability of the basic ideas of four-stranded DNA and base methylation effect to the mechanism of action of modification methylases and other restriction endonucleases was shortly discussed, but only tentative conclusions could be reached.