Within the quasiparticle random-phase approximation (QRPA) we achieve partial restoration of the isospin symmetry and hence fulfillment of the requirement that the 2νββ Fermi matrix element M2ν F vanishes, as it should, unlike in the previous version of the method. This is accomplished by separating the renormalization parameter gpp of the particle-particle proton-neutron interaction into isovector and isoscalar parts. The isovector parameter gT=1pp needs to be chosen to be essentially equal to the pairing constant gpair, so no new parameter is needed. For the 0νββ decay the Fermi matrix element M0νF is substantially reduced, while the full matrix element M0ν is reduced by≈10%. We argue that this more consistent approach should be used from now on in the proton-neutron QRPA and in analogous methods.