The analysis of mass spectrometry data is still largely based on identification of single MS/MS spectra and does not attempt to make use of the extra information available in multiple MS/MS spectra from partially or completely overlapping peptides. Analysis of MS/MS spectra from multiple overlapping peptides opens up the possibility of assembling MS/MS spectra into entire proteins, similarly to the assembly of overlapping DNA reads into entire genomes. In this paper, we present for the first time a way to detect, score, and interpret overlaps between uninterpreted MS/MS spectra in an attempt to sequence entire proteins rather than individual peptides. We show that this approach not only extends the length of reconstructed amino acid sequences but also dramatically improves the quality of de novo peptide sequencing, even for low mass accuracy MS/MS data.