Heterodyne-detected vibrational sum frequency generation spectroscopy was applied to the water surface for measuring the imaginary part of second-order nonlinear susceptibility (Im χ(2)) spectrum in the bend frequency region for the first time. The observed Im χ(2) spectrum shows an overall positive band around 1650 cm-1, contradicting former theoretical predictions. We further found that the Im χ(2) spectrum of NaI aqueous solution exhibits an even larger positive band, which is apparently contrary to the flip-flop orientation of surface water. These unexpected observations are elucidated by calculating quadrupole contributions beyond the conventional dipole approximation. It is indicated that the Im χ(2) spectrum in the bend region has a large quadrupole contribution from the bulk water.