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Within QRPA we achieve partial restoration of the isospin symmetry and hencefulfillment of the requirement that the $2\nu\beta\beta$ Fermi matrix element$M^{2\nu}_F$ vanishes, as it should, unlike in the previous version of themethod. This is accomplished by separating the renormalization parameter$g_{pp}$ of the particle-particle proton-neutron interaction into the isovectorand isoscalar parts. The isovector parameter $g_{pp}^{T=1}$ need to be chosento be essentially equal to the pairing constant $g_{pair}$, so no new parameteris needed. For the $0\nu\beta\beta$ decay the Fermi matrix element $M^{0\nu}_F$is substantially reduced, while the full matrix element $M^{0\nu}$ is reducedby $\approx$ 10%. We argue that this more consistent approach should be usedfrom now on in the proton-neutron QRPA and in analogous methods.

$0\nu\beta\beta$ and $2\nu\beta\beta$ nuclear matrix elements, QRPA, and isospin symmetry restoration