False positive and false negative peaks detected from extracted ion chromatograms (EIC) are an urgent problem with existing software packages that preprocess untargeted liquid or gas chromatography-mass spectrometry metabolomics data because they can translate downstream into spurious or missing compound identifications. We have developed new algorithms that carry out the sequential construction of EICs and detection of EIC peaks. We compare the new algorithms to two popular software packages XCMS and MZmine 2 and present evidence that these new algorithms detect significantly fewer false positives. Regarding the detection of compounds known to be present in the data, the new algorithms perform at least as well as XCMS and MZmine 2. Furthermore, we present evidence that mass tolerance in m/z should be favored rather than mass tolerance in ppm in the process of constructing EICs. The mass tolerance parameter plays a critical role in the EIC construction process and can have immense impact on the detection of EIC peaks.