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The nuclear matrix elements M0ν of the neutrinoless double-beta decay (0νββ) of most nuclei with known 2νββ-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA (RQRPA). The experimental 2νββ-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. With such procedure the M0ν values become essentially independent of single-particle basis size, the axial vector quenching factor, etc. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. It is suggested that most of the spread among the published M0ν's can be ascribed to the choices of implicit and explicit parameters, inherent to the QRPA method.