Signal models where non-negative vector data are represented by a sparse linear combination of non-negative basis vectors have attracted much attention in problems including image classification, document topic modeling, sound source segregation and robust speech recognition. In this paper, an iterative algorithm based on Newton updates to minimize the Kullback-Leibler divergence between data and model is proposed. It finds the sparse activation weights of the basis vectors more efficiently than the expectation-maximization (EM) algorithm. To avoid the computational burden of a matrix inversion, a diagonal approximation is made and therefore the algorithm is called diagonal Newton Algorithm (DNA). It is several times faster than EM, especially for undercomplete problems. But DNA also performs surprisingly well on overcomplete problems.