The one-gluon-exchange interaction includes a contact term, which includes the spin-spin interaction. Such a contact interaction leads to divergent integrals. About combinations of the Fermi-type interactions including the spin-spin interaction, we present a new resort for convergence. In addition to the non-local form factor with 4 end points introduced by Kristensen and Moller, a factor for convergence is introduced. Under a specific combination of the Fermi-type interactions, the wave function is able to be normalized and the eigenvalue is able to be obtained even in the case where the cut-off momentum is taken to be infinity, as the factor for convergence works.