We calculate the cross-section for the excitation and subsequent decay of triple giant resonances (TGDR) in several nuclei excited with heavy ions.The recently developed coherent plus incoherent theory for the excitation in conjunction with the hybrid decay model of Dias-Hussein-Adhikari are used for the purpose. It is emphasized that the direct decay of the TGR is expected to deviate appreciably from the harmonic limit especially at low bombarding energies, owing to the incoherent contribution.