The Faraday B term of magnetic circular dichroism is expressed in terms of single residues of quadratic response functions. These residues contain, however, singularities where the frequency parameter is equal to the excitation energy. The singularities are removed by solving the ill-defined linear response equations in a space orthogonal to the excitation vector. The B terms are calculated for the N --> V pi --> pi* and Rydberg pi --> 3s transitions at the SCF and MCSCF levels for ethylene and for the lowest-lying X(1)A(g) --> 1(1)B(1u) transition in p-benzoquinone at the SCF level. (C) 1999 Elsevier Science B.V. All rights reserved.