We propose a method for the flux calibration of reverberation mapping spectra based on accurate measurement of [O III] $lambda 5007$ emission by spectral fitting. The method can achieve better accuracy than the traditional method of van Groningen & Wanders (1992), allowing reverberation mapping measurements for object with variability amplitudes as low as $sim$ 5%. As a demonstration, we reanalyze the data of the Seyfert 1 galaxy MCG--6-30-15 taken from the 2008 campaign of the Lick AGN Monitoring Project, which previously failed to obtain a time lag for this weakly variable object owing to a relatively large flux calibration uncertainty. We detect a statistically significant rest-frame time lag of $6.38_{-2.69}^{+3.07}$ days between the H$beta$ and $V$-band light curves. Combining this lag with FWHM(H$beta$) = $1933pm81$ $rm km~s^{-1}$ and a virial coefficient of $f$ = 0.7, we derive a virial black hole mass of $3.26_{-1.40}^{+1.59}times10^6$ $M_{odot}$, which agrees well with previous estimates by other methods.
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