A method for the nondestructive read-out of the memory in ferroelectric thin films is demonstrated using the detection second harmonic currents introduced in the ferrolelectric capacitor as a response to an ac signal. The sign and phase of the second harmonic current depends on the polarized state +$P_r or -P_r$, The studied ferroelectric PZT thin film is found to have desirable features for the use as a memory element. This method and material seems as a promising approach for the nonvolatile memory storage.