© Springer International Publishing AG, part of Springer Nature 2018. Tensor decompositions are still in the process of study and development. In this paper, we point out a problem existing in nonnegative tensor decompositions, stemming from the representation of decomposable tensors by outer products of vectors, and propose approaches to solve it. In fact, a scaling indeterminacy appears whereas it is not inherent in the decomposition, and the choice of scaling factors has an impact during the execution of iterative algorithms and should not be overlooked. Computer experiments support the interest in the greedy algorithm proposed, in the case of the CP decomposition.