Decays of the positronium molecule Ps2 into para- or orthopositronium Ps in the ground state and photons are investigated. The differential probabilities of the decays are determined. The total probabilitiesw 2γ (Ps2) andw 3γ (Ps2) of Ps2 annihilation with the production of two and three photons and positronium are calculated to be $$w_{2\gamma }^{(P_{S_2 } )} = 1.6 \cdot 10^{10} \sec ^{ - 1} ,w_{3\gamma }^{(P_{S_2 } )} = 0.43 \cdot 10^8 \sec ^{ - 1} $$ . The curve of the angular correlation of the γ rays on the decay of Ps2 into two photons and parapositronium is studied. The width of this curve is Δ¦P¦=0.128 a.u. (¦P¦ is the total photon momentum), which corresponds to a deviation of the emission angle of the γ rays from π: θ ≲ 0.934 mrad. The maximum in the distribution of the photons with respect to the momenta ¦P¦ in the center of mass of the annihilating pair is attained at ¦P¦=0.175 a.u. The calculations were made on an M-222 computer, and their accuracy is determined by the choice of the wave function of the positronium molecule and the accuracy in the computer calculation of the integrals.