Abstract: According to the infinite product formula of scaling function's Fourier transform，combined with the Fourier transform relation between a function and its Hilbert transform，the paper derived an condition on how two wavelet bases constructed from two conjugate quadrature filters can be pairs of wavelet bases，and proposed a method on how to construct the pairs of wavelet bases.At the same time，a discrete  numerical solution for the filters  h0  and  g0  of minimal length that satisfy the derivate condition was presented.

Key words: Hilbert transform, two scale equation, pairs of wavelets transform, conjugate quadrature filter