A new relation between the maximum geometric concentration factor C and the angular acceptance interval for asymmetrical ideal non-imaging concentrators is proposed. A generalization of the well-known relation for the two-dimensional case, sin theta(c) = 1/C where theta(c) is the acceptance half-angle, results in the proposed relation sin theta(2) - sin theta(1) = 2/C, where theta(1) and theta(2) are the angles of the acceptance interval limits relative to the normal of the entrance aperture. The proposed relation is valid for any ideal 2D concentrator, symmetrical or asymmetrical. A proof based on conservation of phase space is provided. (c) 2005 Elsevier Ltd. All rights reserved.