A complete multiple reciprocity method (CMRM), usually for the eigenvalue analysis of Helmholtz equation, is introduced to the BEM for frequency-dependent inductance extraction. Several approaches are proposed to resolve the problem of "ill-conditioned" series encountered when applying the CMRM practically. Using the BEM combined with CMRM, the major operations of calculating the numerical integrals for a frequency point become reusable, so that inductance extraction for a frequency range is greatly accelerated. Numerical results verify the accuracy and efficiency of the proposed method