Abstract: This paper provides a theory and a method of constructing multivariable non-tensor product biorthogonal wavelets from existing univariable wavelets via direction integral so that the perfect properties of excellent univariable wavelets can be retained.None of the wavlets constructed in this paper is based on Box spline since neither the scaling function nor the dual scaling function constructed in this paper by direction integral is a Box spline.

Key words: multivariable biorthogonal wavelet, non-tensor product, direction integral