Abstract: First, we constructed a periodic multiresolution analys is about the parallel hexagon. Then, using the discrete Fourier transform over 3-direction partition domains, we constructed a kind of bivariate periodic non -tensor-product orthogonal wavelets defined on parallel hexagons. There are only 4 terms in the corresponding refinement equations of the orthogonal scaling functions and the wavelets (and so do the decomposition andreconstruction algorithms). The method presented here is general which is simple for implementation.

Key words: non-tensor-product partition domain, periodic multire solution analysis, refinement equation, periodic wavelets