The ability to quantify the ﬂuorescence signals from multiply labeled biological samples is highly desirable in the life sciences but often difﬁcult, because of spectral overlap between ﬂuorescent species and the presence of autoﬂuorescence. Several so called unmixing algorithms have been developed to address this problem. Here, we present a novel algorithm that combines measurements of lifetime and spectrum to achieve unmixing without a priori information on the spectral properties of the ﬂuorophore labels. The only assumption made is that the lifetimes of the ﬂuorophores differ. Our method combines global analysis for a measurement of lifetime distributions with singular value decomposition to recover individual ﬂuorescence spectra. We demonstrate the technique on simulated datasets and subsequently by an experiment on a biological sample. The method is computationally efﬁcient and straightforward to implement. Applications range from histopathology of complex and multiply labelled samples to functional imaging in live cells.