The Dirac-Van Vleck-Serber method of configuration interaction is applied to formulate the collinear superexchange interaction between V2+ and Ni2+ ions. The major terms of the exchange integral derived by using this method are found to be equivalent to the result of Anderson's mechanism of potential exchange. The dominant contribution to the superexchange interaction is found to arise from the spin polarization of the ligand pσ orbitals via covalent mixing with Ni2+ ions, in cooperation with the direct exchange between the spins of V2+ ions and the polarized pσ orbitals. The strength of the interaction is computed to be 7.3°K (ferromagnetic) for V2+ and Ni2+ ions in MgO, a value which is expected to be too small by a factor of about 2. A semiempirical estimate for the exchange integral is performed for V2+ and Ni2+ ions in KMgF3 by using the measured values for the unpaired spin densities in KNiF3 and V2+:KMgF3. The strength of collinear superexchange is expected to be roughly 15°K for this case.