Under the Jaynes-Cummings model, the evolution of nonclassical properties of two cavity modes is discussed, such as squeezing, sub-Poissonian statistics and violations of Cauchy-Schwarz inequalities and Bell inequalities are discussed. The two cavity modes are initially in pair coherent states, each mode interacts with two two-level atoms resonantly. Numerical simulation results show that some nonclassical properties can be enhanced after resonant interaction between the atoms and the cavity and the performance of a selective atomic measurement. Moreover, after atom-cavity interaction, a resonant classical microwave field is applied to the atoms, which performs a unitary transformation on the atomic states, a selective measurement is performed to the atoms after selecting transform parameters the two-mode squeezing can be somehow enhanced.