The matrix method of Tsai for the calculation of the nonlocal exchange potential has been extended to calculate the plain-wave expanded interstitial part using the Thomas-Fermi damping wave vector. We found enhancement of the 3d-band exchange splitting and consequently the magnetizations and magnetic moments relative to those obtained by LSDA. By resolving the valence electrons of the Fe, Co, and Ni atoms into spin-polarized s, p, and d components, we found depletion of the itinerant 4sp electrons that enhances the minority-spin localized d electrons, which is the main cause of the substantial reduction of the magnetic moments in the metals from those of free atoms. Using idealistic domain-wall-free structural models, the magnetizations of these three metals calculated by the exchange-matrix method are overestimated. The overestimates correlate with the exchange energies, which may play a determinative role in the sizes of domain walls.