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The triple-trap mass spectrometer ISOLTRAP at ISOLDE/CERN has demonstrated the feasibility of mass spectrometry of in-trap-decay product ions. This novel technique gives access to radionuclides, which are not produced directly at ISOL-type radioactive ion beam facilities. As a proof of principle, the in-trap decay of 37K+ has been investigated in a Penning trap filled with helium buffer gas. The half-life of the mother nuclide was confirmed and the recoiling 37Ar+ daughter ion was contained within the trap. The ions of either the mother or the daughter nuclide were transferred to a precision Penning trap, where their mass was determined.