A new class of biorthogonal filter banks, called the even-triplet-halfband-filter-bank (ETHFB), is introduced here. The filters are of even length and have linear phase response. 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. These filters will be 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, i.e., a Hilbert pair. The determination of the design parameters of the filter bank is achieved through an efficient least-squares method.