A new class of biorthogonal filter banks, called the even-triplet-halfband-filter-bank (ETHFB), is introduced here. The filters have even-length, and are used to match a given odd-length filter bank such that the equivalent wavelet functions of both filter banks are approximate Hilbert transform of each other, ie. Hilbert pair. There are two versions of the ETHFB and they are modifications of the (odd-length) triplet-halfband-filter-bank. The parametric Bernstein polynomial is utilized in the construction of the three kernels that define the ETHFB. The determination of the design parameters of the filter bank is achieved through an efficient least squares method