A theory of condensation and resolubilization of a dilute DNA solution with growing concentration of multivalent cations, N, is suggested. It is based on a new theory of screening of a macroion by multivalent cations, which shows that due to strong cation correlations at the surface of DNA the net charge of DNA changes sign at some small concentration of cations N0. DNA condensation takes place in the vicinity of N0, where absolute value of the DNA net charge is small and the correlation induced short range attraction dominates the Coulomb repulsion. At N>N0 positive DNA should move in the opposite direction in an electrophoresis experiment. From comparison of our theory with experimental values of condensation and resolubilization thresholds for DNA solution containing Spe4+, we obtain that N0 = 3.2mM and that the energy of DNA condensation per nucleotide is 0.07 kBT.