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We provide a detailed description of the Herschel-SPIRE Fourier Transform Spectrometer (FTS) Spectral Feature Finder (FF). The FF is an automated process designed to extract significant spectral features from SPIRE FTS data products. Optimising the number of features found in SPIRE-FTS spectra is challenging. The wide SPIRE-FTS frequency range (447-1568 GHz) leads to many molecular species and atomic fine structure lines falling within the observed bands. As the best spectral resolution of the SPIRE-FTS is ~1.2 GHz, there can be significant line blending, depending on the source type. In order to find, both efficiently and reliably, features in spectra associated with a wide range of sources, the FF iteratively searches for peaks over a number of signal-to-noise ratio (SNR) thresholds. For each threshold, newly identified features are rigorously checked before being added to the fitting model. At the end of each iteration, the FF simultaneously fits the continuum and features found, with the resulting residual spectrum used in the next iteration. The final FF products report the frequency of the features found and the associated SNRs. Line flux determination is not included as part of the FF products, as extracting reliable line flux from SPIRE-FTS data is a complex process that requires careful evaluation and analysis of the spectra on a case-by-case basis. The FF results are 100% complete for features with SNR greater than 10 and 50-70% complete at SNR of 5. The FF code and all FF products are publicly available via the Herschel Science Archive.