With this Letter, we complete our model of the Galactic magnetic field (GMF), by using the WMAP7 22 GHz total synchrotron intensity map and our earlier results to obtain a 13-parameter model of the Galactic random field, and to determine the strength of the striated random field. In combination with our 22-parameter description of the regular GMF, we obtain a very good fit to more than 40,000 extragalactic Faraday rotation measures and the WMAP7 22 GHz polarized and total intensity synchrotron emission maps. The data call for a striated component to the random field whose orientation is aligned with the regular field, having zero mean and rms strength approximate to 20% larger than the regular field. A noteworthy feature of the new model is that the regular field has a significant out-of-plane component, which had not been considered earlier. The new GMF model gives a much better description of the totality of data than previous models in the literature.