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First observation of the competitive double-γ decay process is presented. It is a second-order electromagnetic decay mode. The 662-keV decay transition from the 11/2− isomer of 137Ba to its ground state proceeds at a fraction of 2 × 10−6 by simultaneous emission of two γ quanta instead of one. The observed angular correlation and energy distribution of coincident γ quanta are well described by a dominant M2 – E2 and a minor E3 – M1 contribution to the double-γ decay branch. The data were well accounted for by a calculation using the Quasiparticle Phonon Model.