Multivariate polynomials are omnipresent in black-box modelling. They are praised for their flexibility and ease of manipulation yet typically fall short in terms of insight and interpretability. Hence, often an alternative representation is desired. Translating the coupled polynomials into a decoupled form, containing only univariate polynomials has hence become a popular option. In this letter, two new polynomial decoupling techniques are introduced. The features and performance of both methods are illustrated on a nonlinear state-space model identified from data of the forced Duffing oscillator.