In this letter, we present a new feature extraction approach based on third-order statistics (coskewness tensor) called principal skewness analysis (PSA). PSA is the natural extension of principal components analysis from second-order statistics to third-order statistics. The result of PSA is equivalent to that of FastICA when skewness is considered as a non-Gaussian index. Similar to FastICA, PSA also applies the fixed-point method to search the skewness extreme directions. However, when calculating the new projected direction in each iteration, PSA only requires a coskewness tensor, whereas FastICA requires all the pixels to be involved. Therefore, PSA has an advantage over FastICA in speed.