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We investigate the dephasing effect of the Kondo singlet in an Aharonov-Bohm interferometer with a quantum dot coupling to left and right electrodes. By employing the cluster expansions, the equations of motion of Green functions are transformed into the corresponding equation of motion of connected Green functions, which contains the correlation of two conduction electrons beyond the Lacroix approximation. With the method we show that the Kondo resonance is suppressed by phase-sensitive detection of Aharonov-Bohm interferometer. Our numerical results have provided a qualitative explanation with the anomalous features observed in a recent experiment by Avinun-Kalish et al. [Phys. Rev. Lett. 92, 156801 (2004)]. 72.15.Qm, 75.20.Hr Controlled dephasing experiments in mesoscopic devices provide an excellent playground for probing the nature of phase coherence transport and studying the wave-particle duality in quantum mechanics. In the devices, coherence of the quantum dots (QD) was monitored by an Aharonov-Bohm interferometer (ABI), and decoherence was induced by a quantum point contact (QPC). Initially such experiments were performed in the mesoscopic structures based on QD in the Coulomb blockade regime [1,2,3]. Then this kind of experiment was extended to the Kondo regime of QD. In the Kondo regime, a Kondo singlet is formed between the localized spin in a QD and electrons in the electrodes. It was shown that the existence of the QPC plays a role of path-sensitive detector and raises significant suppression of the Kondo resonance [4]. However, properties of the suppression were strongly different from the theoretical prediction of Ref. [5]. The most significant deviation from the theory is that the measured suppression strength of the Kondo resonance is larger 30 times than expected. PACSRecently, to explain the anomalous features, a theory was proposed by K. Kang [6], in which K. Kang thought that the phase-sensitive detection of the QPC is also an important component for the decoherence of the Kondo singlet. We point out that this treatment is incomplete, because the phase-sensitive detection of the QD is performed mainly by the ABI and not by the QPC. Therefore phase-sensitive detection of the ABI should also be taken into account. One way to prove our proposal is to throw off the QPC from the controlled dephasing devices and only to check the influence of phase-sensitive detection of the ABI, then the controlled depasing device becomes an Aharonov-Bohm interferometer with a quantum dot coupling to left and right electrodes, which is designed first by Yacoby [7] to measure the phase sensitivity of a QD. It is just the model that we intend to investigate.In this Letter, we provide a qualitative explanation with the anomalous features observed in a recent dephasing experiment by Avinun-Kalish et al. By employing the cluster expansions, the equations of motion (EOM) of Green's functions are transformed into the corresponding EOM of connected Green's functions, which contains the correlation of two conduction ...