Coherent electronic transport through a double quantum dot (2qd) system connected in a series with electrodes is studied by means of nonequilibrium Green functions and using the equation of motion method, in which all electron correlations in the 2qd are treated exactly. For moderate Coulomb interactions we predict features in a conductance characteristics resulting from transmission through triplet states, which can be strongly activated for larger source-drain voltages. The analysis of the spin-spin correlation functions shows strong antiferromagnetic correlations arising from transport through the singlet state and a reduction of the total magnetic moment. However, when the transmission channel corresponding to the triplet state becomes activated the antiferromagnetic correlations are much weaker, the spins behave as free electrons spins and strongly fluctuate. We speculate that this effect can be seen in wide range of a gate voltage for a double electron occupancy of the 2qd.