This paper presents a novel linear solar concentrating system named BDLFR, acronym of Beam-Down Linear Fresnel Reflector. A BDLFR system consists of a primary LFR array reflecting sunlight into a secondary hyperbolic –or elliptic– cylinder mirror that beams-downs reflected rays to its secondary focal line at ground level, where the receiver is placed. A model based on vector notation –and validated against SolTrace– predicts the optical behavior of BDLFR and generates layouts to avoid blockings. The edge ray approach is utilized to determine receiver aperture widths. As a function of beam-down curvature ratio, the BDLFR configurations that maximize solar collection are found out. Concentration ratios about 80 are reached with a tertiary re-concentrator (CPC) coupled to the receiver aperture.