This paper describes a data preprocessing algorithm that can be used to mitigate the effects of interfering spectral components when the goal is to detect the spectrum of unknown components in a mixture of known components or to verify the presence of suspected components in the spectrum of a mixture of known components. The algorithm is both relatively simple and applicable to a wide range of problems in spectroscopy. The range of applicability can be increased by combining the method with other data preprocessing methods, for example derivative spectra, and can also accommodate variability in the spectra of one or more of the known components. Examples of the application of the algorithm to real problems are given for near-infrared analysis of antibiotic drug formulations inside gelatin capsules and mid-infrared analysis of atmospheric pollutants. Graphical Abstract