The paper is devoted to the development of the asymptotic algorithm for the cloud top height h and the geometrical thickness l determination using measurements of the cloud reflection function. It is based on the asymptotic theory of the radiative transfer in the oxygen absorption bands and simple parameterization of the radiative transport in the atmosphere above and under a cloud. In particular, we have studied the influence of the error of the developed approximate theory on the accuracy of the retrieval of the pair (h, l). It was assumed that there is only a single cloud layer having the same value of the liquid water content in all points inside the cloud. The values (h, l) have been found, solving the inverse problem having as input the synthetic spectra of backscattered light. The synthetic spectra were found using the exact solution of the forward problem for given values of (h, l). The retrieval technique was based on the asymptotic theory. We have found that the error of the cloud top height determination is smaller than 20 m, and the error of the cloud geometrical thickness determination is smaller than 500 m for solar angles 20--70 degrees, values of h in the range 1--12 km, values of geometrical thickness l in the range 0.5--2 km, and values of the cloud optical thickness changing in the range 10--50. The surface albedo has been assumed to be equal zero. We have also studied the influence of the cloud liquid water profile on the results of the retrieval of the pair (h, l). It was found that the error of the cloud top height determination increases up to 600 m, if the assumed cloud has a changing with height liquid water content, and retrievals are made applying the inversion with assumed constant liquid water content profile. The error in the geometrical thickness increases up to 1 km in this case. Errors of the retrieval increase even further if the retrieval, on the basis of the homogeneous layer theory, is applied to the two-layered cloud system (e.g., the upper cloud consists of ice crystals and the lower cloud is in a liquid phase). This signifies the importance of the cloud vertical inhomogeneity on the retrieval results.