Accurate lidar-based measurements of cloud optical extinction, even though perhaps limited to the cloud base region, are useful. Arguably, more advanced lidar techniques (e.g. Raman) should be applied for this purpose. However, simpler polarisation and backscatter lidars offer a number of practical advantages (e.g. better resolution and more continuous and numerous time series). In this paper, we present a backscatter lidar signal inversion method for the retrieval of the cloud optical extinction in the cloud base region. Though a numerically stable method for inverting lidar signals using a far-end boundary value solution has been demonstrated earlier and may be considered as being well established (i.e. the Klett inversion), the application to high-extinction clouds remains problematic. This is due to the inhomogeneous nature of real clouds, the finite range resolution of many practical lidar systems, and multiple scattering effects. We use an inversion scheme, where a backscatter lidar signal is inverted based on the estimated value of cloud extinction at the far end of the cloud, and apply a correction for multiple scattering within the cloud and a range resolution correction. By applying our technique to the inversion of synthetic lidar data, we show that, for a retrieval of up to 90g m from the cloud base, it is possible to obtain the cloud optical extinction within the cloud with an error better than 5g %. In relative terms, the accuracy of the method is smaller at the cloud base but improves with the range within the cloud until 45g m and deteriorates slightly until reaching 90g m from the cloud base.