  In this paper, the ranges of bilinear pseudo-differential operators of
$S_{0,0}$-type on $L^2 \times L^2$ are determined in the framework of Besov
spaces. Our result improves the $L^2 \times L^2 \to L^1$ boundedness of those
operators with symbols in the bilinear H\"ormander class $BS^m_{0,0}$.
