  I propose a new method to determine the strength of the isoscalar
proton-neutron pairing interaction by a mathematical identity derived in the
quasiparticle random-phase approximation. This method is applied for a few
nuclei possibly having the neutrinoless double-$\beta$ decay. Reduced
half-life, the theoretical quantity necessary for determining the effective
neutrino mass, is calculated for $^{48}$Ca.
