  In this paper, we consider the boundedness from $H^{1} \times L^{\infty}$ to
$L^{1}$ of bilinear Fourier integral operators with non-degenerate phase
functions and amplitudes in $BS_{1,0}^{-n/2}$. Our result gives an improvement
of Rodr\'iguez-L\'opez, Rule, and Staubach's result.
