A kinematically complete measurement of the four-body breakup reaction d +d~d*+d*~p +n +p +n has been performed at 15.7 MeV bombarding energy. A ring-detector system consisting of a charged-particle detector and a neutron detector is used to define a singlet deuteron, i.e. , d*; a charged-particle detector is used to measure spectra of products produced by another d* at five angles. A velocity-distribution diagram has first been obtained, and by performing a fit the most probable breakup energy of the singlet deuteron in the laboratory system is obtained, 0.054+0.012 MeV.A final state interaction calculation using known p-n singlet phase shifts predicts the expected proton spectra.PACS number(s):