A Hilbert pair is defined as a pair of wavelet functions that are approximate Hilbert transform of each other. This paper presents the design of the corresponding pair of filter banks that defines (generate) these wavelets. The filters have exact linear phase which yields biorthogonal wavelets with exact symmetry. The technique is based on matching a given even-length filter bank with an odd-length filter bank. The class of THFB (triplet halfband filter bank) is utilized in the matching design. The parameteric Bernstein is used for the construction of the three kernels that define the THFB and the perfect reconstruction and vanishing moments properties are structurally imposed. A least-least squares formulation of the design problem is used and this yields good results.