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The CRESST experiment (Cryogenic Rare Event Search with Superconducting Thermometers) uses CaWO4 single crystals as targets for the direct search of dark matter particles. For rare event experiments, low intrinsic contaminations of the crystals play a crucial role. Since several years CaWO4 crystals are grown at the Technische Universität München (TUM). Commercially available CaCO3 and WO3 powders are used for the synthesis of CaWO4 powder. In order to improve the radiopurity of the crystals, it is necessary to reduce potential sources of radioactive materials such as U, Th, Sr and Pb in CaWO4 powder. In this poster, we present our studies of the chemical purification of raw materials and a new method to synthesize high purity CaWO4 powder. This research was supported by the DFG cluster of excellence "Origin and Structure of the Universe", Boltzmannstr. 2, 85748 Garching, by the Helmholtz Alliance for Astroparticle Physics, by the Maier-Leibnitz-Laboratorium (Garching) and by the BMBF.