We mainly consider the case that one of the two entangled atoms with two energy levels interacts with a single-mode and double-photon cavity field. The atom is selectively detected after exiting the cavity, and it is found that the noncla ssical properties of field states depend strongly on the entanglement degree bet ween the two atoms. Meanwhile, it is proved that the squeezing of the field and the photon antibunching can be greatly enhanced via selective atomic measurement s.