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Ground-state and finite-temperature properties of the square-lattice S= 1/2 Heisenberg model with antiferromagnetic nearest-and next-nearest-neighbor interactions (J 1− J 2 model) are investigated by a spin-rotation-invariant Green’s-function theory, where a reasonable agreement with numerical diagonalization data is found. The quantum phase transitions from the Néel and collinear phases into a spin-liquid phase are obtained at (J 2/J 1) c 1= 0.24 and (J 2/J 1) c 2= 0.83, respectively, which considerably improves the results by a previous similar approach. The low-temperature magnetic susceptibility at J 2/J 1≲ 0. 5, the temperature of the susceptibility maximum, and the antiferromagnetic correlation length are found to decrease with increasing frustration. For high-T c cuprates the relationship between the t− J model and an effective J 1− J 2 model is analyzed.