We propose a new linear method for dimension reduction to identify non- Gaussian components in high dimensional data. Our method, NGCA (non-Gaussian component analysis), uses a very general semi-parametric framework. In contrast to existing projection methods we define what is uninteresting (Gaussian): by projecting out uninterestingness, we can estimate the relevant non-Gaussian subspace. We show that the estimation error of finding the non-Gaussian components tends to zero at a parametric rate. Once NGCA components are identified and extracted, various tasks can be applied in the data analysis process, like data visualization, clustering, denoising or classification. A numerical study demonstrates the usefulness of our method.