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In this study, the authors propose a novel construction frame of lifting scheme, which includes corresponding filters design, theory analysis and application. By applying the presented frame, they can realise the lifting scheme of biorthogonal wavelets with prediction and updating filters that are of arbitrary odd or even length. The prediction and updating filters are built based on Bernstein bases and generalised Bernstein bases, which possess transforming characters of symmetry, required vanishing moments and flatness of passbands of frequency response. The authors further obtain a new family of biorthogonal wavelets and the related library of biorthogonal symmetric waveforms. By using the parametric filters, they can achieve the best transform possible aiming at image compression by adjusting the coefficients of the filters. The authors explore the applicability of the proposed transforms for image compression with high compression rates, and the results of the experiments show that the performance is comparable with CDF9/7.