Fluorescence microscopy and genetically encoded calcium indicators help understand brain function by recording large-scale in vivo videos in assorted animal models. Extracting the fluorescent transients that represent active periods of individual neurons is a key step when analyzing imaging videos. Non-specific calcium sources and background adjacent to segmented neurons contaminate the neurons’ temporal traces with false transients. We developed and characterized a novel method, temporal unmixing of calcium traces (TUnCaT), to quickly and accurately unmix the calcium signals of neighboring neurons and background. Our algorithm used background subtraction to remove the false transients caused by background fluctuations, and then applied targeted non-negative matrix factorization to remove the false transients caused by neighboring calcium sources. TUnCaT was more accurate than existing algorithms when processing multiple experimental and simulated datasets. TUnCaT’s speed was faster than or comparable to existing algorithms.