We calculated electronic matrix elements for hole transfer between adjacent nucleobases in DNA. Calculations of the matrix elements for intrastrand and interstrand transfer were performed at the Hartree-Fock level employing the 6-31G* and 6-311G** basis sets. The matrix elements for intrastrand hole transfer, for which a wealth of experimental solution data is available, are almost independent of the basis set and exhibit an exponential interbase distance dependence, sensitivity to the donor-acceptor geometry, and dependence on 5′ → 3′ direction base sequence. The calculated intrastrand hole transfer matrix elements between adjacent thymines, v+(T, T) = 0.16 eV, is in good agreement with the experimental estimate, v+(T, T) = 0.18 eV, inferred from hole hopping in G+(T)mGGG (m = 1-3). The features of the nucleobase bridge specificity for superexchange-induced hole hopping between guanines in G+XY...G (X, Y = T or A) were elucidated, with the prediction of enhanced efficiency of thymine relative to adenine as mediator. Information on superexchange-mediated intrastrand and direct interstrand hole hopping between guanine bases was also inferred. Our results for interstrand, adjacent G+G coupling predict the existence of zigzagging pathways for hole hopping, in line with experiment.