The potential describing long-range interactions between D0-branes contains spin-dependent terms. In the matrix model, these should be reproduced by the one-loop effective action computed in the presence of a non-trivial fermionic background psi. The upsilon(3)psi(2)/r(8) term in the effective action has been computed by Kraus and shown to correspond to a spin-orbit interaction between D0-branes, and the psi(8)/r(11) term in the static potential has been obtained by Barrio et al. In this paper, the upsilon(2)psi(4)/r(9) term is computing in the matrix model and compared with the corresponding results of Morales et al. obtained using string theoretic methods. The technique employed is adapted to the underlying supersymmetry of the matrix model, and should be useful in the calculation of spin-dependent effects in more general Dp-brane scatterings, (C) 1998 Elsevier Science B.V.