The N-FINDR algorithm has been widely used in hyperspectral image analysis for endmember extraction due to its simplicity and effectiveness. However, there are several disadvantages of implementing the N-FINDR. This letter proposes an algorithm for decomposition of mixed pixels. It improves the N-FINDR in several aspects. First, an iterative Gram-Schmidt orthogonalization is applied in the endmember searching process to replace the matrix determinant calculation used in N-FINDR, which makes this algorithm run very fast and can also guarantee the stability of its final results. Second, with the set of orthogonal bases obtained by the Gram-Schmidt orthogonalization, the algorithm can also help to estimate the proper number of endmembers and unmix the original images by itself. In addition, unlike the N-FINDR, a dimensionality reduction transform is not necessary in this algorithm. Experimental results of both simulated images and practical remote sensing images demonstrate that this algorithm is a fast and accurate algorithm for the decomposition of mixed pixels.