Non-Gaussian component analysis (NGCA) is an unsupervised linear dimension reduction method that extracts low-dimensional non-Gaussian "signals" from high-dimensional data contaminated with Gaussian noise. NGCA can be regarded as a generalization of projection pursuit (PP) and independent component analysis (ICA) to multidimensional and dependent non-Gaussian components. Indeed, seminal approaches to NGCA are based on PP and ICA. Recently, a novel NGCA approach called least-squares NGCA (LSNGCA) has been developed, which gives a solution analytically through least-squares estimation of logdensity gradients and eigendecomposition. However, since pre-whitening of data is involved in LSNGCA, it performs unreliably when the data covariance matrix is ill-conditioned, which is often the case in highdimensional data analysis. In this paper, we propose a whitening-free variant of LSNGCA and experimentally demonstrate its superiority.