Abstract: Lifting scheme, which is a new approach of constructing the second-generation wavelets, can also be used to construct first-generation ones. Compared with Daubechiess construction approach, lifting scheme can easily be grasped by readers who are not well equipped with Fourier analysis. The following fact will be proved using Lawton matrix in this paper: almost all wavelets constructed using lifting scheme satisfy the biorthogonal condition. Another topic in this paper is to ensure linear-phase property of new ones. Some examples are given to demonstrate how to construct linear-phase biorthogonal wavelets.