A new algorithm to estimate lidar ratios of aerosol layers with a monochromatic Mic-scattering lidar profile is proposed. The algorithm employs both the forward,and the backward solutions of the monochromatic single-scattering lidar equation. The lidar ratios are estimated through an iterative procedure to match the two solutions by correcting a lidar ratio assigned at the beginning of the procedure. The algorithm has been applied to simulated lidar profiles and a measured one from the literature. In testing of the simulated profiles, the estimation errors of the lidar ratios were investigated for four boundary conditions-clear to turbid conditions-by scanning boundary values and extinction coefficients of an aerosol layer. This investigation indicated that the algorithm estimates the lidar ratio with sufficient accuracy under clear boundary conditions even with inaccurate boundary values, but requires correct boundary values under turbid boundary conditions. The algorithm was successfully applied to the measured lidar profile of a thin aerosol layer. The obtained lidar ratio was reasonably plausible. This suggests that an enhanced form of this algorithm using the forward and the backward solutions would be able to determine the lidar ratios and boundary values from only a lidar profile measured under arbitrary atmospheric conditions.