The dynamic relationship between beat-to-beat mean arterial blood pressure (ABP) fluctuations and cerebral blood flow velocity (CBFV) variations have been intensively studied. The experimentally observed low coherence in the low-frequency band has previously indicated that the assumptions of linearity and/or stationarity, the preconditions of the linear transfer function analysis, are not valid in that frequency region. Latka et al. [M. Latka, M. Turalska, M. Glaubic-Latka, W. Kolodziej, D. Latka, and B. J. J. West, "Phase dynamics in cerebral autoregulation," Amer. J. Physiol. Heart Circ. Physiol., vol. 289 pp. H2272-H2279, Jul. 2005] used a wavelet phase synchronization method to identify the instantaneous phase difference between ABP and CBFV, and low values of synchronization index were found in the low-frequency range, seeming to provide further evidence that the cerebral autoregulation system is nonstationary. Here, we focus on another possible factor corresponding for this low synchronization index-unmeasured variability. We demonstrate analytically and with a physiologically based cerebral hemodynamic model that, in the case of multiple inputs, the phase difference between one input, ABP, and the output, CBFV, will be distorted by an additional input, end-tidal CO(2) (P(ETCO(2))), and no longer accurately represent the true ABP-CBFV system phase shift. We also prove that this phase distortion can be corrected if the transfer functions for ABP-CBFV and P(ETCO(2))-CBFV are known or can be estimated. A significantly increased value of synchronization index in the low-frequency band is found by using the CO(2) correction term with experimental data on 13 subjects. This essentially indicates that the lack of synchronization between ABP and CBFV previously identified by Latka et al. [M. Latka, M. Turalska, M. Glaubic-Latka, W. Kolodziej, D. Latka, and B. J. J. West, "Phase dynamics in cerebral autoregulation," Amer. J. Physiol. Heart Circ. Physiol., vol. 289, pp. H2272-H2279, Jul. 2005] can be partly attributed to unmeasured variability.