In a previous work from Ansmann et al., 1992, Appl. Opt., 31(33), p. 7123, a range-independent lidar ratio estimation method was qualitatively proposed by iteratively solving the lidar equation in forward and backward form in a cloud layer. The method provides independent aerosol extinction and backscatter using a simple backscatter lidar. Here, the method is analytically re-formulated in terms of an objective function (whose root is the sought-after lidar ratio) ready to be solved by conventional numerical techniques. A 532-nm case example is discussed.