This Letter is part of an effort to use the Curl equations to calculate non-adiabatic coupling terms, subject to ab initio boundary conditions. As examples we consider two-state, planar, systems characterized by two coordinates, theta and q and treat the corresponding non-adiabatic coupling terms, namely tau(theta)(q, theta) and tau(q)(q, theta). The theory, which yields tau(q)(q, theta) once tau(theta)(q, theta) is given, is applied to three cases: an analytical model and two ab initio treatments - one for the C2H molecule and one for the, H + H-2 molecular system. In all three cases encouraging agreements were obtained between the theoretical tau(q)(q, theta) values and the ab initio ones. (C)2002 Elsevier Science B.V. All rights reserved.