Multiresolution analysis (MRA) and wavelets provide useful and efficient tools for representing functions at multiple levels of details. Wavelet representations have been used in a broad range of applications, including image compression, physical simulation and numerical analysis. In this paper, the authors construct a new class of wavelets, called four-point wavelets,based on an interpolatory four-point subdivision scheme. They are of local support, symmetric and stable. The analysis and synthesis algorithms have linear time complexity. Depending on different weight parameters w, the scaling functions and wavelets generated by the four-point subdivision scheme are of different degrees of smoothness. Therefore the user can select better wavelets relevant to the practice among the classes of wavelets. The authors apply the fourpoint wavelets in signal compression. The results show that the four-point wavelets behave much better than B-spline wavelets in many situations.