Nonadiabatic variational calculations for the positronium molecule, Ps(2) = (e(+)e(-))(2), a cluster composed of two electrons and two positrons, is the subject of theoretical investigation. In particular, calculations of the two-photon annihilation rate as well as estimation of the lifetime at the nonrelativistic level of theory are presented in detail. In all calculations the nonadiabatic four-body wave function is expanded in terms of explicitly correlated Gaussian functions. The energy of the center-of-mass motion is effectively eliminated from the total nonrelativistic energy through the modified variational principle based on the internal Hamiltonian. With the wave function expanded in terms of 300 basis functions, which leads to a total energy equal to -0.515 980 au and a binding energy equal to 0.435 eV, the lifetime of the system is estimated to be 0.907 ns.