A total-field/scattered-field (TF/SF) boundary for the constrained interpolation profile (CIP) method is proposed for multi-dimensional electromagnetic problems. Incident fields are added to or subtracted from update equations in order to satisfy advection equations into which Maxwell's equations are reduced by means of the directional splitting. Modified incident fields are introduced to take into account electromagnetic fields after advection. The developed TF/SF boundary is examined numerically, and the results show that it operates with good performance. Finally, we apply the proposed TF/SF boundary to a scattering problem, and it can be solved successfully.