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With partially restored isospin symmetry, we calculate the nuclear matrixelement for a special decay mode of $2\nu\beta\beta$ (two neutrino double betadecay) -- the decay to the first $2^+$ excited states. With the realisticCD-Bonn nuclear force, we analyze the dependence of the nuclear matrix elementson the iso-vector and iso-scalar parts of proton-neutron particle-particleinteraction. The dependence on the different nuclear matrix element is observedand the results are explained. We also give the phase space factors withnumerical electron wave functions and properly chosen excitation energies.Finally we give our results for the half-lives of this decay mode for differentnuclei.

$2\nu\beta\beta$-decay to first $2^+$ state with partial isospin symmetry restoration from spherical QRPA calculations