Causal discovery is the task of finding plausible causal relationships from statistical data [1,2]. Such methods rely on various assumptions about the data generating process to identify it from uncontrolled observations. We have recently proposed a causal discovery method based on independent component analysis (ICA) called LiNGAM [3], showing how to completely identify the data generating process under the assumptions of linearity, non-gaussianity, and no hidden variables. In this paper, after briefly recapitulating this approach, we focus on the algorithmic problems encountered when the number of variables considered is large. Thus we extend the applicability of the method to data sets with tens of variables or more. Experiments confirm the performance of the proposed algorithms, implemented as part of the latest version of our freely available Matlab/Octave LiNGAM package.