Abstract. Given a biorthogonal pair of multi-resolution analyses on the interval, by integration or differentiation, we build a new biorthogonal pair of multiresolution analyses. Using both pairs, isotropic or, as we focus on, anisotropic divergence-free wavelet bases on the hypercube are constructed. Our construction generalizes the one from [Rev. Mat. Iberoamericana, 8 (1992), pp. 221–237] by...