This paper introduces a new biorthogonal wavelet based on a variant of √2 subdivision by using the lifting scheme. The greatest advantage of this wavelet is its very slow gradual refinement for quadrilateral meshes, which offers the biggest number of resolution levels to control a quadrilateral mesh. Moreover, the resulting wavelet transforms have a linear computational complexity, as they are composed of local and in-place lifting operations only. Feature lines can also be effectively integrated into the wavelet transforms as self-governed boundary curves. The introduced wavelet analysis can be used in a variety of applications such as progressive transmission, data compression, shape approximation and multiresolution rendering. The experiments have shown sufficient stability as well as better performance of the introduced wavelet analysis, as compared to the existing wavelet analyses for quadrilateral meshes of arbitrary topology.