A new algorithm is developed to solve integral equations for simple liquids. The algorithm is based on the discrete wavelet transform of radial distribution functions. The Coifman 2 basis set is employed for the wavelet treatment. To solve integral equations we have applied the combined scheme in which the coarse part of the solution is calculated by wavelets, while the fine part by the direct iterations. Tests on the PY and HNC approximations have indicated that the proposed procedure is more effective than the conventional method based on the hybrid algorithm. Possibilities for application of the method to molecular liquids and mixed quantum-classical systems are discussed. (C) 2004 American Institute of Physics.