In a previous Letter, Kuczera's theory of the canonical force field was generalized to the case of redundant curvilinear internal coordinates related by non-linear constraints. A central issue in this theory is the projection from the space of internal coordinates onto the pure vibrational manifold. In this Letter we present a new mathematical treatment of the projection that solves some problems of inconsistency that have arisen when applying the theory to molecules with a central atom. In addition to solving these problems, this treatment greatly simplifies the attainment of the projection and, consequently, the calculation of canonical force constants. (C) 2010 Elsevier B.V. All rights reserved.