  We present a generator-coordinate calculation, based on a relativistic
energy-density functional, of the low-lying spectra in the isotopes $^{150}$Nd
and $^{150}$Sm and of the nuclear matrix element that governs the neutrinoless
double-beta decay of the first isotope to the second. We carefully examine the
impact of octupole correlations on both nuclear structure and the double-beta
decay matrix element. Octupole correlations turn out to reduce quadrupole
collectivity in both nuclei. Shape fluctuations, however, dilute the effects of
octupole deformation on the double-beta decay matrix element, so that the
overall octupole-induced quenching is only about 7\%.
