  We consider the bilinear pseudo-differential operators with symbols in the
bilinear H\"ormander classes $BS_{\rho, \rho}^m$, $0 < \rho < 1$. In this
paper, we show that the condition $1/p = 1/p_1 + 1/p_2$ is necessary when we
consider the boudnedness from $H^{p_1} \times H^{p_2}$ to $L^p$ of those
operators for the critical case.
