In this paper, a fast incremental principal non-Gaussian directions analysis algorithm, called IPCA-ICA, is introduced. This algorithm computes the principal components of a sequence of image vectors incrementally without estimating the covariance matrix (so covariance-free) and at the same time transforming these principal components to the independent directions that maximize the non-Gaussianity of the source. Two major techniques are used sequentially in a real-time fashion in order to obtain the most efficient and independent components that describe a whole set of human faces database. This procedure is done by merging the runs of two algorithms based on principal component analysis (PCA) and independent component analysis (ICA) running sequentially. This algorithm is applied to face recognition problem. Simulation results on different databases showed high average success rate of this algorithm compared to others.