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This paper presents a projection pursuit (PP) based method for blind separation of nonnegative sources. First, the available observation matrix is mapped to construct a new mixing model, in which the inaccessible source matrix is normalized to be column-sum-to-1. Then, the PP method is proposed to solve this new model, where the mixing matrix is estimated column by column through tracing the projections to the mapped observations in specified directions, which leads to the recovery of the sources. The proposed method is much faster than Chan's method, which has similar assumptions to ours, due to the usage of optimal projection. It is also more advantageous in separating cross-correlated sources than the independence- and uncorrelation-based methods, as it does not employ any statistical information of the sources. Furthermore, the new method does not require the mixing matrix to be nonnegative. Simulation results demonstrate the superior performance of our method.