A new two-dimensional concentrator for solar energy collection has been developed. The concentrator has the following advantages, when compared with the classic Compound Parabolic Concentrators invented by Roland Winston, W. T Welford, A. Rabl, Baranov, and other researchers: 1) It allows the use of parabolic mirrors, which have a reflecting area much smaller for a given concentration ratio and acceptance angle. 2) Between the mirror and the absorber there is a large gap so that conduction losses are reduced. Convection losses can be reduced, too, if the absorber is enclosed within a glass tube. 3) It can be easily manufactured. Instead of seeking the shape of the mirrors for a given shape of the absorber we have made the inverse statement of the problem, and we have obtained the optimal shapes of the absorbers with a prescribed acceptance angle, for parabolic mirrors, assuming that the intercept factor is unity, the mirrors are perfect, and the absorber surfaces are convex. The concentrator should be east-west oriented, and could be seasonal or monthly tilt adjusted. This concentrator could have many practical applications, such as fluid heating, steam generation, etc.